Finite Group Databasebeta

← Group #10823533

Character table — Group #10823533

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222222234444444444446666666121212121212121288888888121212121212121224242424242424242424242424242424244466888812121212121224242424242424242222444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1
χ9111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1
χ10111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111
χ11111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ12111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ13111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ14111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ15111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-1-1-1
χ16111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111
χ172222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000000002-2-22220000-2-222-2-2000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000-222-2-2-2000022-2-222000000000000000000000000
χ19222222222-2-2-2-22222-2-2-2-22222222-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000000000002-22-2220000-2-2-2-222000000000000000000000000
χ20222222222-2-2-2-22222-2-2-2-22222222-2-2-2-2-2-2-2-200000000-2-2-2-222220000000000000000-22-22-2-200002222-2-2000000000000000000000000
χ2122222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211-2-2-2-2111111111111110000000000000000
χ2322222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-1-1-2-2-2-2-1-1-1-1-1-1111111110000000000000000
χ2422222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2112222111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-111113333−3−3−3−33333−3−3−3−32-2-22-1-1000011-1-11133−3−333−3−30000000000000000
χ2622222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-111113333−3−3−3−33333−3−3−3−3-222-2110000-1-111-1-1−3−333−3−3330000000000000000
χ2722222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-11111−3−3−3−33333−3−3−3−333332-2-22-1-1000011-1-111−3−333−3−3330000000000000000
χ2822222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111100000000-1-1-1-11111−3−3−3−33333−3−3−3−33333-222-2110000-1-111-1-133−3−333−3−30000000000000000
χ2922222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-111111111000000001111-1-1-1-13333−3−3−3−3−3−3−3−333332-22-2-1-100001111-1-133−3−3−3−3330000000000000000
χ3022222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-111111111000000001111-1-1-1-13333−3−3−3−3−3−3−3−33333-22-22110000-1-1-1-111−3−33333−3−30000000000000000
χ3122222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-111111111000000001111-1-1-1-1−3−3−3−333333333−3−3−3−32-22-2-1-100001111-1-1−3−33333−3−30000000000000000
χ3222222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-111111111000000001111-1-1-1-1−3−3−3−333333333−3−3−3−3-22-22110000-1-1-1-11133−3−3−3−3330000000000000000
χ3322222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-11111111122-2-2-1-122-2-2-1-11111-1-1-1-111110000000000000000
χ3422222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2-22211-2-22211-1-1-1-11111-1-1-1-10000000000000000
χ3522222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-122-2-2-1-1-2-222-1-111111111-1-1-1-10000000000000000
χ3622222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-2-2221122-2-211-1-1-1-1-1-1-1-111110000000000000000
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χ3822-22-22-2-222i2i−2i−2i2i2i−2i−2i22-2-222-2-22-2-22222-2-2-2-2000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000-22−2i2i00000000
χ3922-22-22-2-222i2i−2i−2i−2i−2i2i2i-2-22222-2-22-2-2-2-2-2-22222000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000002-2002i−2i
χ4022-22-22-2-222i2i−2i−2i−2i−2i2i2i-2-22222-2-22-2-2-2-2-2-22222000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000000000-2200−2i2i
χ4122-22-22-2-22−2i−2i2i2i2i2i−2i−2i-2-22222-2-22-2-2-2-2-2-2222200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000002-200−2i2i
χ4222-22-22-2-22−2i−2i2i2i2i2i−2i−2i-2-22222-2-22-2-2-2-2-2-2222200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000000000-22002i−2i
χ4322-22-22-2-22−2i−2i2i2i−2i−2i2i2i22-2-222-2-22-2-22222-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000002-2−2i2i00000000
χ4422-22-22-2-22−2i−2i2i2i−2i−2i2i2i22-2-222-2-22-2-22222-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000-222i−2i00000000
χ452-22-222-2-222i−2i2i−2i2i−2i2i−2i2-22-2-2-2222-2-222-2-222-2-2000000002i−2i2i−2i2i−2i2i−2i00000000000000000000002-22i−2i0000002-22-22i−2i2i−2i0000000000000000
χ462-22-222-2-222i−2i2i−2i2i−2i2i−2i2-22-2-2-2222-2-222-2-222-2-2000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000-22−2i2i000000-22-22−2i2i−2i2i0000000000000000
χ472-22-222-2-222i−2i2i−2i−2i2i−2i2i-22-22-2-2222-2-2-2-222-2-2222i2i−2i−2i22-2-22i−2i2i−2i−2i2i−2i2i2i2i−2i−2i2i2i−2i−2i22-2-222-2-20000000000000000000000000000000000000000
χ482-22-222-2-222i−2i2i−2i−2i2i−2i2i-22-22-2-2222-2-2-2-222-2-222−2i−2i2i2i-2-2222i−2i2i−2i−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i-2-222-2-2220000000000000000000000000000000000000000
χ492-22-222-2-22−2i2i−2i2i2i−2i2i−2i-22-22-2-2222-2-2-2-222-2-2222i2i−2i−2i-2-222−2i2i−2i2i2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i-2-222-2-2220000000000000000000000000000000000000000
χ502-22-222-2-22−2i2i−2i2i2i−2i2i−2i-22-22-2-2222-2-2-2-222-2-222−2i−2i2i2i22-2-2−2i2i−2i2i2i−2i2i−2i−2i−2i2i2i−2i−2i2i2i22-2-222-2-20000000000000000000000000000000000000000
χ512-22-222-2-22−2i2i−2i2i−2i2i−2i2i2-22-2-2-2222-2-222-2-222-2-200000000−2i2i−2i2i−2i2i−2i2i00000000000000000000002-2−2i2i0000002-22-2−2i2i−2i2i0000000000000000
χ522-22-222-2-22−2i2i−2i2i−2i2i−2i2i2-22-2-2-2222-2-222-2-222-2-200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000-222i−2i000000-22-222i−2i2i−2i0000000000000000
χ532-22-222-2-2-12i−2i2i−2i2i−2i2i−2i2-22-211-1-1-111-1-111-1-11100000000−ii−ii−ii−ii−i3−i3i3i3i3i3−i3−i3−3−33333−3−30000−i3i32-22i−2i−i3i33−33−3-11-11−ii−ii0000000000000000
χ542-22-222-2-2-12i−2i2i−2i2i−2i2i−2i2-22-211-1-1-111-1-111-1-11100000000−ii−ii−ii−ii−i3−i3i3i3i3i3−i3−i3−3−33333−3−30000i3−i3-22−2i2ii3−i3−33−331-11-1i−ii−i0000000000000000
χ552-22-222-2-2-12i−2i2i−2i2i−2i2i−2i2-22-211-1-1-111-1-111-1-11100000000−ii−ii−ii−iii3i3−i3−i3−i3−i3i3i333−3−3−3−3330000−i3i3-22−2i2i−i3i33−33−31-11-1i−ii−i0000000000000000
χ562-22-222-2-2-12i−2i2i−2i2i−2i2i−2i2-22-211-1-1-111-1-111-1-11100000000−ii−ii−ii−iii3i3−i3−i3−i3−i3i3i333−3−3−3−3330000i3−i32-22i−2ii3−i3−33−33-11-11−ii−ii0000000000000000
χ572-22-222-2-2-12i−2i2i−2i−2i2i−2i2i-22-2211-1-1-11111-1-111-1-12i2i−2i−2i22-2-2−ii−iii−ii−i−i−iii−i−iii-1-111-1-1110000−i3i30000i3−i33−3−333−3−33i3−i3−i3i30000000000000000
χ582-22-222-2-2-12i−2i2i−2i−2i2i−2i2i-22-2211-1-1-11111-1-111-1-12i2i−2i−2i22-2-2−ii−iii−ii−i−i−iii−i−iii-1-111-1-1110000i3−i30000−i3i3−333−3−333−3−i3i3i3−i30000000000000000
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χ602-22-222-2-2-12i−2i2i−2i−2i2i−2i2i-22-2211-1-1-11111-1-111-1-1−2i−2i2i2i-2-222−ii−iii−ii−iii−i−iii−i−i11-1-111-1-10000i3−i30000−i3i3−333−33−3−33i3−i3−i3i30000000000000000
χ612-22-222-2-2-1−2i2i−2i2i2i−2i2i−2i-22-2211-1-1-11111-1-111-1-12i2i−2i−2i-2-222i−ii−i−ii−ii−i−iii−i−iii11-1-111-1-10000−i3i30000i3−i3−333−33−3−33−i3i3i3−i30000000000000000
χ622-22-222-2-2-1−2i2i−2i2i2i−2i2i−2i-22-2211-1-1-11111-1-111-1-12i2i−2i−2i-2-222i−ii−i−ii−ii−i−iii−i−iii11-1-111-1-10000i3−i30000−i3i33−3−33−333−3i3−i3−i3i30000000000000000
χ632-22-222-2-2-1−2i2i−2i2i2i−2i2i−2i-22-2211-1-1-11111-1-111-1-1−2i−2i2i2i22-2-2i−ii−i−ii−iiii−i−iii−i−i-1-111-1-1110000−i3i30000i3−i3−333−3−333−3i3−i3−i3i30000000000000000
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χ672-22-222-2-2-1−2i2i−2i2i−2i2i−2i2i2-22-211-1-1-111-1-111-1-11100000000i−ii−ii−ii−ii3i3−i3−i3−i3−i3i3i3−3−33333−3−30000−i3i3-222i−2i−i3i3−33−331-11-1−ii−ii0000000000000000
χ682-22-222-2-2-1−2i2i−2i2i−2i2i−2i2i2-22-211-1-1-111-1-111-1-11100000000i−ii−ii−ii−ii3i3−i3−i3−i3−i3i3i3−3−33333−3−30000i3−i32-2−2i2ii3−i33−33−3-11-11i−ii−i0000000000000000
χ692-2-2-2-222222-2-222-2-222-2-22-2-2-2-222222-2-2-2-222000000002-2-222-2-220000000000000000000000000000000000000000002-200002-2000000
χ702-2-2-2-222222-2-222-2-222-2-22-2-2-2-222222-2-2-2-222000000002-2-222-2-22000000000000000000000000000000000000000000-220000-22000000
χ712-2-2-2-222222-2-22-222-2-222-2-2-2-2-2222-2-22222-2-2000000002-2-22-222-200000000000000000000000000000000000000002-200000000002-200
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χ732-2-2-2-22222-222-22-2-22-222-2-2-2-2-2222-2-22222-2-200000000-222-22-2-2200000000000000000000000000000000000000002-20000000000-2200
χ742-2-2-2-22222-222-22-2-22-222-2-2-2-2-2222-2-22222-2-200000000-222-22-2-220000000000000000000000000000000000000000-2200000000002-200
χ752-2-2-2-22222-222-2-222-22-2-22-2-2-2-222222-2-2-2-22200000000-222-2-222-20000000000000000000000000000000000000000002-20000-22000000
χ762-2-2-2-22222-222-2-222-22-2-22-2-2-2-222222-2-2-2-22200000000-222-2-222-2000000000000000000000000000000000000000000-2200002-2000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.