Finite Group Databasebeta

← Group #10729235

Character table — Group #10729235

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order12222222222222223444444446666666666666664444444412121212121212121212121212121212121212121212121222224444666666661212121212121212444444444444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ1011111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ1111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ1211111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ1311111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ1411111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1511111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1611111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ172222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ182222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ192222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-222-2-2-1-1-1-11111-1-1-1-11111000000000000000000000000
χ202222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-222-2-2221111-1-1-1-11111-1-1-1-1000000000000000000000000
χ212222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ222222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ232222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-1000000000000000000000000
χ242222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-11111000000000000000000000000
χ2522222-2-22-22-2-2-2-22-220000000022222-2-2-2-2-2-22-2-22000022-2-200000000000000002222-2-2-2-20000000000000000000000002i2i−2i−2i000000002i2i−2i−2i00000000
χ2622222-2-22-22-2-2-2-22-220000000022222-2-2-2-2-2-22-2-22000022-2-200000000000000002222-2-2-2-2000000000000000000000000−2i−2i2i2i00000000−2i−2i2i2i00000000
χ2722222-2-22-22-2-2-2-22-220000000022222-2-2-2-2-2-22-2-220000-2-2220000000000000000-2-2-2-222220000000000000000000000002i2i−2i−2i00000000−2i−2i2i2i00000000
χ2822222-2-22-22-2-2-2-22-220000000022222-2-2-2-2-2-22-2-220000-2-2220000000000000000-2-2-2-22222000000000000000000000000−2i−2i2i2i000000002i2i−2i−2i00000000
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χ332222-2-2-2-22-222-2-2-22-12i2i2i2i−2i−2i−2i−2i-1-1-111-1-1-11111-11100000000−i−i−i−iiiii−i3−i3−i3−i3i3i3i3i333−3−333−3−3002-2002i−2i−i3−i3i3i3-1-11133−3−3−i−iii000000000000000000000000
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χ362222-2-2-2-22-222-2-2-22-12i2i2i2i−2i−2i−2i−2i-1-1-111-1-1-11111-11100000000−i−i−i−iiiiii3i3i3i3−i3−i3−i3−i3−3−333−3−33300-2200−2i2i−i3−i3i3i311-1-133−3−3ii−i−i000000000000000000000000
χ372222-2-2-2-22-222-2-2-22-1−2i−2i−2i−2i2i2i2i2i-1-1-111-1-1-11111-11100000000iiii−i−i−i−i−i3−i3−i3−i3i3i3i3i3−3−333−3−333002-200−2i2i−i3−i3i3i3-1-111−3−333ii−i−i000000000000000000000000
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χ4122-2-2222-22-22-2-2-22-22000000002-2-22-22-2-222-2-22-2222-2-200000000000022-2-222-2-20000000000000000000000000000000000002i2i−2i−2i00002i−2i2i−2i00000000
χ4222-2-2222-22-22-2-2-22-22000000002-2-22-22-2-222-2-22-2222-2-200000000000022-2-222-2-2000000000000000000000000000000000000−2i−2i2i2i0000−2i2i−2i2i00000000
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χ4622-2-22-2-2-2-2-2-222222222-2-222-2-22-2-22-2-222-2-22-2-2220000000022-2-222-2-2000000000000000000000000000000000000000000000000-2-222-222-200000000
χ4722-2-22-2-2-2-2-2-2222222-2-222-2-2222-2-22-2-222-2-22-2-22200000000-2-222-2-22200000000000000000000000000000000000000000000000022-2-2-222-200000000
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χ4922-2-2-2222-22-22-2-2-2222i2i−2i−2i−2i−2i2i2i2-2-2-22-22222-22-2-2-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000000000002i−2i2-20000
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χ562-22-222-222-2-22-22-2-2200000000-22-22-2-22-22-2-2222-2-22-22000000000000-22-22-22-2200000000000000000000000000000000−2i2i−2i2i00002i−2i2i−2i000000000000
χ572-22-22-222-2-22-22-2-2222i−2i2i−2i2i−2i2i−2i-22-22-22-22-2222-2-2-2000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000002-2-222i−2i2i−2i0000000000000000
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χ652-2-2222-2-222-2-22-2-2222i−2i−2i2i2i−2i−2i2i-2-2222-2-222-22-22-2-22-2-222i−2i2i−2i2i−2i−2i2i2i−2i−2i2i2-2-222-2-222i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000
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χ732-2-2222-2-222-2-22-2-22-1−2i2i2i−2i−2i2i2i−2i11-1-1-111-1-11-11-1112-2-22−2i2i−2i2ii−i−iii−i−ii-111-1-111-1i−ii−ii−ii−i00000000−i3i3−i3i3−i3i3−i3i3−33−33−33−33000000000000000000000000
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χ762-2-2222-2-222-2-22-2-22-1−2i2i2i−2i−2i2i2i−2i11-1-1-111-1-11-11-111-222-22i−2i2i−2ii−i−iii−i−ii1-1-111-1-11−ii−ii−ii−ii00000000i3−i3i3−i3−i3i3−i3i33−33−3−33−33000000000000000000000000
χ772-2-222-22-2-2222-22-2-2200000000-2-222222-2-22-2-2-22-200002i−2i−2i2i00000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000002-2-222i−2i−2i2i000000000000
χ782-2-222-22-2-2222-22-2-2200000000-2-222222-2-22-2-2-22-200002i−2i−2i2i00000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000-222-2−2i2i2i−2i000000000000
χ792-2-222-22-2-2222-22-2-2200000000-2-222222-2-22-2-2-22-20000−2i2i2i−2i0000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000002-2-22−2i2i2i−2i000000000000
χ802-2-222-22-2-2222-22-2-2200000000-2-222222-2-22-2-2-22-20000−2i2i2i−2i0000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000-222-22i−2i−2i2i000000000000
χ812-2-22-2-2222-2-2-2-222222-2-22-222-2-2-22-2-2-2-22-22-22222000000002-2-22-222-200000000000000002-2002-2002-2-2200002-2-220000000000000000000000000000
χ822-2-22-2-2222-2-2-2-222222-2-22-222-2-2-22-2-2-2-22-22-22222000000002-2-22-222-20000000000000000-2200-2200-222-20000-222-20000000000000000000000000000
χ832-2-22-2-2222-2-2-2-22222-222-22-2-22-2-22-2-2-2-22-22-2222200000000-222-22-2-2200000000000000002-200-22002-2-220000-222-20000000000000000000000000000
χ842-2-22-2-2222-2-2-2-22222-222-22-2-22-2-22-2-2-2-22-22-2222200000000-222-22-2-220000000000000000-22002-200-222-200002-2-220000000000000000000000000000
χ852-2-22-2-2222-2-2-2-2222-12-2-22-222-211-11111-11-11-1-1-1-100000000-111-11-1-11−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i32-2002-200-111-1−i3i3i3−i3-111-1−i3i3i3−i3000000000000000000000000
χ862-2-22-2-2222-2-2-2-2222-12-2-22-222-211-11111-11-11-1-1-1-100000000-111-11-1-11−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3-2200-22001-1-11i3−i3−i3i31-1-11i3−i3−i3i3000000000000000000000000
χ872-2-22-2-2222-2-2-2-2222-12-2-22-222-211-11111-11-11-1-1-1-100000000-111-11-1-11i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i32-2002-200-111-1i3−i3−i3i3-111-1i3−i3−i3i3000000000000000000000000
χ882-2-22-2-2222-2-2-2-2222-12-2-22-222-211-11111-11-11-1-1-1-100000000-111-11-1-11i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3-2200-22001-1-11−i3i3i3−i31-1-11−i3i3i3−i3000000000000000000000000
χ892-2-22-2-2222-2-2-2-2222-1-222-22-2-2211-11111-11-11-1-1-1-1000000001-1-11-111-1−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i32-200-2200-111-1−i3i3i3−i31-1-11i3−i3−i3i3000000000000000000000000
χ902-2-22-2-2222-2-2-2-2222-1-222-22-2-2211-11111-11-11-1-1-1-1000000001-1-11-111-1−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3-22002-2001-1-11i3−i3−i3i3-111-1−i3i3i3−i3000000000000000000000000
χ912-2-22-2-2222-2-2-2-2222-1-222-22-2-2211-11111-11-11-1-1-1-1000000001-1-11-111-1i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i32-200-2200-111-1i3−i3−i3i31-1-11−i3i3i3−i3000000000000000000000000
χ922-2-22-2-2222-2-2-2-2222-1-222-22-2-2211-11111-11-11-1-1-1-1000000001-1-11-111-1i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3-22002-2001-1-11−i3i3i3−i3-111-1i3−i3−i3i3000000000000000000000000
χ9344444-4-44-44-4-4-4-44-4-200000000-2-2-2-2-2222222-222-2000044-4-40000000000000000-2-2-2-22222000000000000000000000000000000000000000000000000
χ9444444-4-44-44-4-4-4-44-4-200000000-2-2-2-2-2222222-222-20000-4-44400000000000000002222-2-2-2-2000000000000000000000000000000000000000000000000
χ954444-444-4-4-4-4-444-4-4400000000444-4-4-4-4-4444-4-44-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ964444-444-4-4-4-4-444-4-4-200000000-2-2-222222-2-2-222-220000000000000000000000002323−23−23−23−232323000000000000000000000000000000000000000000000000
χ974444-444-4-4-4-4-444-4-4-200000000-2-2-222222-2-2-222-22000000000000000000000000−23−2323232323−23−23000000000000000000000000000000000000000000000000
χ9844-4-4444-44-44-4-4-44-4-200000000-222-22-222-2-222-22-244-4-4000000000000-2-222-2-22200000000000000000000000000000000000000000000000000000000
χ9944-4-4444-44-44-4-4-44-4-200000000-222-22-222-2-222-22-2-4-44400000000000022-2-222-2-200000000000000000000000000000000000000000000000000000000
χ10044-4-44-4-4-4-4-4-444444-244-4-444-4-4-222-222-2-222-222-2-200000000-2-222-2-2220000000000000000000000000000000000000000000000000000000000000000
χ10144-4-44-4-4-4-4-4-444444-2-4-444-4-444-222-222-2-222-222-2-20000000022-2-222-2-20000000000000000000000000000000000000000000000000000000000000000
χ10244-4-4-4444-44-44-4-4-44-24i4i−4i−4i−4i−4i4i4i-2222-22-2-2-2-22-222200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ10344-4-4-4444-44-44-4-4-44-2−4i−4i4i4i4i4i−4i−4i-2222-22-2-2-2-22-2222000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000000000000000
χ10444-4-4-4-4-44444-444-4-44000000004-4-4-444-4-4-4-44444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10544-4-4-4-4-44444-444-4-4-200000000-2222-2-22222-2-2-2-220000000000000000−2i3−2i32i32i32i32i3−2i3−2i300000000000000000000000000000000000000000000000000000000
χ10644-4-4-4-4-44444-444-4-4-200000000-2222-2-22222-2-2-2-2200000000000000002i32i3−2i3−2i3−2i3−2i32i32i300000000000000000000000000000000000000000000000000000000
χ1074-44-444-444-4-44-44-4-4-2000000002-22-222-22-222-2-2-224-44-4000000000000-22-22-22-2200000000000000000000000000000000000000000000000000000000
χ1084-44-444-444-4-44-44-4-4-2000000002-22-222-22-222-2-2-22-44-440000000000002-22-22-22-200000000000000000000000000000000000000000000000000000000
χ1094-44-44-444-4-44-44-4-44-24i−4i4i−4i4i−4i4i−4i2-22-22-22-22-2-2-222200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000000000
χ1104-44-44-444-4-44-44-4-44-2−4i4i−4i4i−4i4i−4i4i2-22-22-22-22-2-2-2222000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ1114-44-4-44-4-4-444-4-4444-24-44-4-44-442-222-2-22-2-22222-2-200000000-22-222-22-20000000000000000000000000000000000000000000000000000000000000000
χ1124-44-4-44-4-4-444-4-4444-2-44-444-44-42-222-2-22-2-22222-2-2000000002-22-2-22-220000000000000000000000000000000000000000000000000000000000000000
χ1134-44-4-4-44-444-444-44-4400000000-44-4-44-44-4-444-44-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1144-44-4-4-44-444-444-44-4-2000000002-222-22-222-2-22-22-20000000000000000−2i32i3−2i32i32i3−2i32i3−2i300000000000000000000000000000000000000000000000000000000
χ1154-44-4-4-44-444-444-44-4-2000000002-222-22-222-2-22-22-200000000000000002i3−2i32i3−2i3−2i32i3−2i32i300000000000000000000000000000000000000000000000000000000
χ1164-4-444-44-4-4444-44-4-4-20000000022-2-2-2-2-222-2222-2200004i−4i−4i4i0000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000000000
χ1174-4-444-44-4-4444-44-4-4-20000000022-2-2-2-2-222-2222-220000−4i4i4i−4i00000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000000000
χ1184-4-44-44-44-4-4444-44-4400000000-4-44-4-444-44-444-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1194-4-44-44-44-4-4444-44-4-20000000022-222-2-22-22-2-222-2000000000000000000000000−2i32i32i3−2i32i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ1204-4-44-44-44-4-4444-44-4-20000000022-222-2-22-22-2-222-20000000000000000000000002i3−2i3−2i32i3−2i32i32i3−2i3000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).