Finite Group Databasebeta

← Group #10729057

Character table — Group #10729057

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order122222222222222234444444466666666666666644444444121212121212121212121212121212121212121212121212224444446666121212121212121212121212222244444444444422444444
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
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ911111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ1011111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ1111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ1211111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111
χ1311111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1411111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1511111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1611111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
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
χ192222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-2-2-222-1-1-1-1-1-1-1-111111111000000000000000000000000
χ202222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-22222-2-211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ212222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-11111-1-1-1-11111000000000000000000000000
χ222222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2-2-2-222221111-1-1-1-11111-1-1-1-1000000000000000000000000
χ232222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-111111111-1-1-1-1000000000000000000000000
χ242222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-1-1-1-1-11111000000000000000000000000
χ25222222-22-2-2-2-2-2-2-2220000000022222-2-2-2-222-2-2-2-22i2i−2i−2i0000000000002i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000002i2i−2i−2i22-2-200000000
χ26222222-22-2-2-2-2-2-2-2220000000022222-2-2-2-222-2-2-2-22i2i−2i−2i0000000000002i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000−2i−2i2i2i-2-22200000000
χ27222222-22-2-2-2-2-2-2-2220000000022222-2-2-2-222-2-2-2-2−2i−2i2i2i000000000000−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000002i2i−2i−2i-2-22200000000
χ28222222-22-2-2-2-2-2-2-2220000000022222-2-2-2-222-2-2-2-2−2i−2i2i2i000000000000−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000−2i−2i2i2i22-2-200000000
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χ352222-2-2-2-2-222-222-2-22−2i−2i−2i−2i2i2i2i2i222-2-2-2-222-2-2-2-22200000000−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000022-2-20000−2i2i2i−2i000000000000
χ362222-2-2-2-2-222-222-2-22−2i−2i−2i−2i2i2i2i2i222-2-2-2-222-2-2-2-22200000000−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000-2-22200002i−2i−2i2i000000000000
χ3722-2-2222-2-22-2-22-22-22000000002-2-2222-22-2-2-22-22-22i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000002-22-22i−2i2i−2i0000000000000000
χ3822-2-2222-2-22-2-22-22-22000000002-2-2222-22-2-2-22-22-22i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000-22-22−2i2i−2i2i0000000000000000
χ3922-2-2222-2-22-2-22-22-22000000002-2-2222-22-2-2-22-22-2−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000002-22-2−2i2i−2i2i0000000000000000
χ4022-2-2222-2-22-2-22-22-22000000002-2-2222-22-2-2-22-22-2−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000-22-222i−2i2i−2i0000000000000000
χ4122-2-222-2-22-222-22-2-222i2i−2i−2i2i2i−2i−2i2-2-222-22-22-2-2-22-222-2-222i−2i2i−2i2i2i−2i−2i2i2i−2i−2i22-2-2-2-2222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ4222-2-222-2-22-222-22-2-222i2i−2i−2i2i2i−2i−2i2-2-222-22-22-2-2-22-22-222-2−2i2i−2i2i2i2i−2i−2i2i2i−2i−2i-2-22222-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ4322-2-222-2-22-222-22-2-22−2i−2i2i2i−2i−2i2i2i2-2-222-22-22-2-2-22-222-2-22−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i22-2-2-2-222−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ4422-2-222-2-22-222-22-2-22−2i−2i2i2i−2i−2i2i2i2-2-222-22-22-2-2-22-22-222-22i−2i2i−2i−2i−2i2i2i−2i−2i2i2i-2-22222-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ4522-2-222-2-22-222-22-2-2-12i2i−2i−2i2i2i−2i−2i-111-1-11-11-1111-11-12-2-222i−2i2i−2i−i−iii−i−iii-1-11111-1-1−i−iii−i−iii00000000−i3−i3i3i333−3−3−i3−i3i3i333−3−3000000000000000000000000
χ4622-2-222-2-22-222-22-2-2-12i2i−2i−2i2i2i−2i−2i-111-1-11-11-1111-11-12-2-222i−2i2i−2i−i−iii−i−iii-1-11111-1-1−i−iii−i−iii00000000i3i3−i3−i3−3−333i3i3−i3−i3−3−333000000000000000000000000
χ4722-2-222-2-22-222-22-2-2-12i2i−2i−2i2i2i−2i−2i-111-1-11-11-1111-11-1-222-2−2i2i−2i2i−i−iii−i−iii11-1-1-1-111ii−i−iii−i−i00000000−i3−i3i3i333−3−3i3i3−i3−i3−3−333000000000000000000000000
χ4822-2-222-2-22-222-22-2-2-12i2i−2i−2i2i2i−2i−2i-111-1-11-11-1111-11-1-222-2−2i2i−2i2i−i−iii−i−iii11-1-1-1-111ii−i−iii−i−i00000000i3i3−i3−i3−3−333−i3−i3i3i333−3−3000000000000000000000000
χ4922-2-222-2-22-222-22-2-2-1−2i−2i2i2i−2i−2i2i2i-111-1-11-11-1111-11-12-2-22−2i2i−2i2iii−i−iii−i−i-1-11111-1-1ii−i−iii−i−i00000000−i3−i3i3i3−3−333−i3−i3i3i3−3−333000000000000000000000000
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χ5222-2-222-2-22-222-22-2-2-1−2i−2i2i2i−2i−2i2i2i-111-1-11-11-1111-11-1-222-22i−2i2i−2iii−i−iii−i−i11-1-1-1-111−i−iii−i−iii00000000i3i3−i3−i333−3−3−i3−i3i3i3−3−333000000000000000000000000
χ5322-2-2-2-222-2-22-2-2222222-2-2-2-2222-2-2-2-22-2-22222-2-220000000022-2-2-2-222000000000000000000000000000000000000000000002-2-2200002-22-200000000
χ5422-2-2-2-222-2-22-2-2222222-2-2-2-2222-2-2-2-22-2-22222-2-220000000022-2-2-2-22200000000000000000000000000000000000000000000-222-20000-22-2200000000
χ5522-2-2-2-222-2-22-2-22222-2-22222-2-22-2-2-2-22-2-22222-2-2200000000-2-22222-2-2000000000000000000000000000000000000000000002-2-220000-22-2200000000
χ5622-2-2-2-222-2-22-2-22222-2-22222-2-22-2-2-2-22-2-22222-2-2200000000-2-22222-2-200000000000000000000000000000000000000000000-222-200002-22-200000000
χ5722-2-2-2-2-2222-222-2-222000000002-2-2-2-2-222-222-222-200002-2-22000000000000000022-2-2-2-2220000000000000000000000002-2-2200000000-222-200000000
χ5822-2-2-2-2-2222-222-2-222000000002-2-2-2-2-222-222-222-200002-2-22000000000000000022-2-2-2-222000000000000000000000000-222-2000000002-2-2200000000
χ5922-2-2-2-2-2222-222-2-222000000002-2-2-2-2-222-222-222-20000-222-20000000000000000-2-22222-2-20000000000000000000000002-2-22000000002-2-2200000000
χ6022-2-2-2-2-2222-222-2-222000000002-2-2-2-2-222-222-222-20000-222-20000000000000000-2-22222-2-2000000000000000000000000-222-200000000-222-200000000
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χ652-22-2-22-2-2-2-2-22222222-22-2-22-22-22-2-22-2222-222-2-2-2000000002-22-2-22-2200000000000000002-200002-22-22-22-22-200000000000000000000000000000000
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χ692-22-2-22-2-2-2-2-222222-12-22-2-22-221-111-11-1-1-11-1-111100000000-11-111-11-13−33−33−33−33−33−33−33−32-200002-2-11-11-11-113−33−33−33−3000000000000000000000000
χ702-22-2-22-2-2-2-2-222222-12-22-2-22-221-111-11-1-1-11-1-111100000000-11-111-11-13−33−33−33−33−33−33−33−3-220000-221-11-11-11-1−33−33−33−33000000000000000000000000
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χ722-22-2-22-2-2-2-2-222222-12-22-2-22-221-111-11-1-1-11-1-111100000000-11-111-11-1−33−33−33−33−33−33−33−33-220000-221-11-11-11-13−33−33−33−3000000000000000000000000
χ732-22-2-22-2-2-2-2-222222-1-22-222-22-21-111-11-1-1-11-1-1111000000001-11-1-11-113−33−33−33−3−33−33−33−332-20000-22-11-111-11-13−33−3−33−33000000000000000000000000
χ742-22-2-22-2-2-2-2-222222-1-22-222-22-21-111-11-1-1-11-1-1111000000001-11-1-11-113−33−33−33−3−33−33−33−33-2200002-21-11-1-11-11−33−333−33−3000000000000000000000000
χ752-22-2-22-2-2-2-2-222222-1-22-222-22-21-111-11-1-1-11-1-1111000000001-11-1-11-11−33−33−33−333−33−33−33−32-20000-22-11-111-11-1−33−333−33−3000000000000000000000000
χ762-22-2-22-2-2-2-2-222222-1-22-222-22-21-111-11-1-1-11-1-1111000000001-11-1-11-11−33−33−33−333−33−33−33−3-2200002-21-11-1-11-113−33−3−33−33000000000000000000000000
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χ912-2-22-2222-22-22-22-2-2-1−2i2i2i−2i2i−2i−2i2i11-11-1-1-11-1-1111-1100000000i−i−ii−iii−i−333−33−3−33i3−i3−i3i3i3−i3−i3i3002i−2i-2200i3−i3−i3i33−3−33−iii−i-111-1000000000000000000000000
χ922-2-22-2222-22-22-22-2-2-1−2i2i2i−2i2i−2i−2i2i11-11-1-1-11-1-1111-1100000000i−i−ii−iii−i−333−33−3−33i3−i3−i3i3i3−i3−i3i300−2i2i2-200−i3i3i3−i3−333−3i−i−ii1-1-11000000000000000000000000
χ93444444-44-4-4-4-4-4-4-44-200000000-2-2-2-2-22222-2-222224i4i−4i−4i000000000000−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000000000000000000000
χ94444444-44-4-4-4-4-4-4-44-200000000-2-2-2-2-22222-2-22222−4i−4i4i4i0000000000002i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000000000000000000000
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χ984444-4-4-4-4-444-444-4-4-2−4i−4i−4i−4i4i4i4i4i-2-2-22222-2-22222-2-2000000002i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ9944-4-4444-4-44-4-44-44-4-200000000-222-2-2-22-2222-22-224i−4i4i−4i000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
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χ10144-4-4-4-444-4-44-4-4444-244-4-4-4-444-22222-222-2-2-2-222-200000000-2-22222-2-20000000000000000000000000000000000000000000000000000000000000000
χ10244-4-4-4-444-4-44-4-4444-2-4-44444-4-4-22222-222-2-2-2-222-20000000022-2-2-2-2220000000000000000000000000000000000000000000000000000000000000000
χ10344-4-4-4-4-4444-444-4-44-200000000-222222-2-22-2-22-2-2200004-4-440000000000000000-2-22222-2-2000000000000000000000000000000000000000000000000
χ10444-4-4-4-4-4444-444-4-44-200000000-222222-2-22-2-22-2-220000-444-4000000000000000022-2-2-2-222000000000000000000000000000000000000000000000000
χ1054-44-44-4444-4-4-444-4-4-24i−4i4i−4i4i−4i4i−4i2-22-22-22-2-2-222-22200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000000000
χ1064-44-44-4444-4-4-444-4-4-2−4i4i−4i4i−4i4i−4i4i2-22-22-22-2-2-222-222000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ1074-44-44-4-44-4444-4-44-4400000000-44-44-4-44-4-44-44-44400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1084-44-44-4-44-4444-4-44-4-2000000002-22-222-222-22-22-2-2000000000000000000000000−2i32i3−2i32i32i3−2i32i3−2i3000000000000000000000000000000000000000000000000
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χ1134-4-444-44-4-4-4444-4-44400000000-4-444-4444-4-44-4-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1144-4-444-44-4-4-4444-4-44-20000000022-2-22-2-2-222-2222-200000000000000000000000023−23−2323−232323−23000000000000000000000000000000000000000000000000
χ1154-4-444-44-4-4-4444-4-44-20000000022-2-22-2-2-222-2222-2000000000000000000000000−232323−2323−23−2323000000000000000000000000000000000000000000000000
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χ1174-4-444-4-4-444-4-4-4444-2-444-4-444-422-2-22222-22-2-2-2-22000000002-2-222-2-220000000000000000000000000000000000000000000000000000000000000000
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χ1204-4-44-44-444-44-44-44-4-20000000022-22-222-22-22-2-22-200000000000000002i3−2i3−2i32i32i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000

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