Finite Group Databasebeta

← Group #10823488

Character table — Group #10823488

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222222234444444444446666666121212121212121288888888121212121212121224242424242424242424242424242424244466888812121212121224242424242424242222444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1111111-1-1-1-111-1-1
χ9111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-11111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ10111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ11111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-11111-1-1-1-111111111-1-11111-1-1-1-1-1-1
χ12111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1111111
χ13111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1
χ14111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111
χ15111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-11111
χ16111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1-1-1
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
χ19222222222-2-2-2-22222-2-2-2-22222222-2-2-2-2-2-2-2-200000000-2-2-2-22222000000000000000022-2-2220000-2-2-2-222000000000000000000000000
χ20222222222-2-2-2-22222-2-2-2-22222222-2-2-2-2-2-2-2-200000000-2-2-2-222220000000000000000-2-222-2-200002222-2-2000000000000000000000000
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
χ2922222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-111111111000000001111-1-1-1-13333−3−3−3−3−3−3−3−3333322-2-2-1-100001111-1-133−3−3−3−3330000000000000000
χ3022222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-111111111000000001111-1-1-1-13333−3−3−3−3−3−3−3−33333-2-222110000-1-1-1-111−3−33333−3−30000000000000000
χ3122222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-111111111000000001111-1-1-1-1−3−3−3−333333333−3−3−3−322-2-2-1-100001111-1-1−3−33333−3−30000000000000000
χ3222222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-111111111000000001111-1-1-1-1−3−3−3−333333333−3−3−3−3-2-222110000-1-1-1-11133−3−3−3−3330000000000000000
χ3322222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-1111111112-22-2-1-122-2-2-1-11111-1-1-1-111110000000000000000
χ3422222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-22-2211-2-22211-1-1-1-11111-1-1-1-10000000000000000
χ3522222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-12-22-2-1-1-2-222-1-111111111-1-1-1-10000000000000000
χ3622222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-22-221122-2-211-1-1-1-1-1-1-1-111110000000000000000
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χ3822-2-22-22-222i2i−2i−2i2i2i−2i−2i22-2-222-2-22-2-22222-2-2-2-2000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000-2200000000−2i2i0000
χ3922-2-22-22-222i2i−2i−2i−2i−2i2i2i-2-22222-2-22-2-2-2-2-2-22222000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000002-22i−2i00000000
χ4022-2-22-22-222i2i−2i−2i−2i−2i2i2i-2-22222-2-22-2-2-2-2-2-22222000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000-22−2i2i00000000
χ4122-2-22-22-22−2i−2i2i2i2i2i−2i−2i-2-22222-2-22-2-2-2-2-2-2222200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000002-2−2i2i00000000
χ4222-2-22-22-22−2i−2i2i2i2i2i−2i−2i-2-22222-2-22-2-2-2-2-2-2222200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000-222i−2i00000000
χ4322-2-22-22-22−2i−2i2i2i−2i−2i2i2i22-2-222-2-22-2-22222-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000002-200000000−2i2i0000
χ4422-2-22-22-22−2i−2i2i2i−2i−2i2i2i22-2-222-2-22-2-22222-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000-22000000002i−2i0000
χ452-22-2-222-222i−2i2i−2i2i−2i2i−2i2-22-2-2-2222-2-222-2-222-2-2000000002i−2i2i−2i2i−2i2i−2i00000000000000000000002i−2i2-20000002i−2i2i−2i2-22-20000000000000000
χ462-22-2-222-222i−2i2i−2i2i−2i2i−2i2-22-2-2-2222-2-222-2-222-2-2000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000−2i2i-22000000−2i2i−2i2i-22-220000000000000000
χ472-22-2-222-222i−2i2i−2i−2i2i−2i2i-22-22-2-2222-2-2-2-222-2-22222-2-22i2i−2i−2i2i−2i2i−2i−2i2i−2i2i22-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ482-22-2-222-222i−2i2i−2i−2i2i−2i2i-22-22-2-2222-2-2-2-222-2-222-2-222−2i−2i2i2i2i−2i2i−2i−2i2i−2i2i-2-222-2-222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ492-22-2-222-22−2i2i−2i2i2i−2i2i−2i-22-22-2-2222-2-2-2-222-2-22222-2-2−2i−2i2i2i−2i2i−2i2i2i−2i2i−2i22-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ502-22-2-222-22−2i2i−2i2i2i−2i2i−2i-22-22-2-2222-2-2-2-222-2-222-2-2222i2i−2i−2i−2i2i−2i2i2i−2i2i−2i-2-222-2-2222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ512-22-2-222-22−2i2i−2i2i−2i2i−2i2i2-22-2-2-2222-2-222-2-222-2-200000000−2i2i−2i2i−2i2i−2i2i00000000000000000000002i−2i-220000002i−2i2i−2i-22-220000000000000000
χ522-22-2-222-22−2i2i−2i2i−2i2i−2i2i2-22-2-2-2222-2-222-2-222-2-200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000−2i2i2-2000000−2i2i−2i2i2-22-20000000000000000
χ532-22-2-222-2-12i−2i2i−2i2i−2i2i−2i2-22-211-1-1-111-1-111-1-11100000000−ii−ii−ii−ii33−3−3−3−333i3i3−i3−i3−i3−i3i3i30000−i3i32i−2i2-2−i3i33−33−3−ii−ii-11-110000000000000000
χ542-22-2-222-2-12i−2i2i−2i2i−2i2i−2i2-22-211-1-1-111-1-111-1-11100000000−ii−ii−ii−ii33−3−3−3−333i3i3−i3−i3−i3−i3i3i30000i3−i3−2i2i-22i3−i3−33−33i−ii−i1-11-10000000000000000
χ552-22-2-222-2-12i−2i2i−2i2i−2i2i−2i2-22-211-1-1-111-1-111-1-11100000000−ii−ii−ii−ii−3−33333−3−3−i3−i3i3i3i3i3−i3−i30000−i3i3−2i2i-22−i3i33−33−3i−ii−i1-11-10000000000000000
χ562-22-2-222-2-12i−2i2i−2i2i−2i2i−2i2-22-211-1-1-111-1-111-1-11100000000−ii−ii−ii−ii−3−33333−3−3−i3−i3i3i3i3i3−i3−i30000i3−i32i−2i2-2i3−i3−33−33−ii−ii-11-110000000000000000
χ572-22-2-222-2-12i−2i2i−2i−2i2i−2i2i-22-2211-1-1-11111-1-111-1-122-2-22i2i−2i−2i−ii−iii−ii−i-1-111-1-111−i−iii−i−iii0000−i3i30000i3−i33−3−33−i3i3i3−i3−333−30000000000000000
χ582-22-2-222-2-12i−2i2i−2i−2i2i−2i2i-22-2211-1-1-11111-1-111-1-122-2-22i2i−2i−2i−ii−iii−ii−i-1-111-1-111−i−iii−i−iii0000i3−i30000−i3i3−333−3i3−i3−i3i33−3−330000000000000000
χ592-22-2-222-2-12i−2i2i−2i−2i2i−2i2i-22-2211-1-1-11111-1-111-1-1-2-222−2i−2i2i2i−ii−iii−ii−i11-1-111-1-1ii−i−iii−i−i0000−i3i30000i3−i33−3−33i3−i3−i3i33−3−330000000000000000
χ602-22-2-222-2-12i−2i2i−2i−2i2i−2i2i-22-2211-1-1-11111-1-111-1-1-2-222−2i−2i2i2i−ii−iii−ii−i11-1-111-1-1ii−i−iii−i−i0000i3−i30000−i3i3−333−3−i3i3i3−i3−333−30000000000000000
χ612-22-2-222-2-1−2i2i−2i2i2i−2i2i−2i-22-2211-1-1-11111-1-111-1-122-2-2−2i−2i2i2ii−ii−i−ii−ii-1-111-1-111ii−i−iii−i−i0000−i3i30000i3−i3−333−3−i3i3i3−i33−3−330000000000000000
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χ632-22-2-222-2-1−2i2i−2i2i2i−2i2i−2i-22-2211-1-1-11111-1-111-1-1-2-2222i2i−2i−2ii−ii−i−ii−ii11-1-111-1-1−i−iii−i−iii0000−i3i30000i3−i3−333−3i3−i3−i3i3−333−30000000000000000
χ642-22-2-222-2-1−2i2i−2i2i2i−2i2i−2i-22-2211-1-1-11111-1-111-1-1-2-2222i2i−2i−2ii−ii−i−ii−ii11-1-111-1-1−i−iii−i−iii0000i3−i30000−i3i33−3−33−i3i3i3−i33−3−330000000000000000
χ652-22-2-222-2-1−2i2i−2i2i−2i2i−2i2i2-22-211-1-1-111-1-111-1-11100000000i−ii−ii−ii−i33−3−3−3−333−i3−i3i3i3i3i3−i3−i30000−i3i32i−2i-22−i3i3−33−33−ii−ii1-11-10000000000000000
χ662-22-2-222-2-1−2i2i−2i2i−2i2i−2i2i2-22-211-1-1-111-1-111-1-11100000000i−ii−ii−ii−i33−3−3−3−333−i3−i3i3i3i3i3−i3−i30000i3−i3−2i2i2-2i3−i33−33−3i−ii−i-11-110000000000000000
χ672-22-2-222-2-1−2i2i−2i2i−2i2i−2i2i2-22-211-1-1-111-1-111-1-11100000000i−ii−ii−ii−i−3−33333−3−3i3i3−i3−i3−i3−i3i3i30000−i3i3−2i2i2-2−i3i3−33−33i−ii−i-11-110000000000000000
χ682-22-2-222-2-1−2i2i−2i2i−2i2i−2i2i2-22-211-1-1-111-1-111-1-11100000000i−ii−ii−ii−i−3−33333−3−3i3i3−i3−i3−i3−i3i3i30000i3−i32i−2i-22i3−i33−33−3−ii−ii1-11-10000000000000000
χ692-2-22-2-22222-2-222-2-222-2-22-2-2-2-222222-2-2-2-222000000002-2-222-2-220000000000000000000000000000000000000000000000002-200002-2
χ702-2-22-2-22222-2-222-2-222-2-22-2-2-2-222222-2-2-2-222000000002-2-222-2-22000000000000000000000000000000000000000000000000-220000-22
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χ722-2-22-2-22222-2-22-222-2-222-2-2-2-2-2222-2-22222-2-2000000002-2-22-222-2000000000000000000000000000000000000000000-2200000000-2200
χ732-2-22-2-2222-222-22-2-22-222-2-2-2-2-2222-2-22222-2-200000000-222-22-2-220000000000000000000000000000000000000000002-200000000-2200
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χ8344-4-44-44-4-24i4i−4i−4i4i4i−4i−4i44-4-4-2-222-222-2-2-2-2222200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ8444-4-44-44-4-24i4i−4i−4i−4i−4i4i4i-4-444-2-222-2222222-2-2-2-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
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χ8644-4-44-44-4-2−4i−4i4i4i−4i−4i4i4i44-4-4-2-222-222-2-2-2-22222000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ8744-4-4-44-4440000000000004-4-44-4-4400000000000022−2222−22000000000000000022−2222−2222−2222−220000000000000000000000000000000000000000
χ8844-4-4-44-4440000000000004-4-44-4-44000000000000−2222−22220000000000000000−2222−2222−2222−22220000000000000000000000000000000000000000
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χ1044-4-4444-4-4-20000000000002-22-22-22−232323−2323−23−232300002i2−2i2−2i22i20000000000000000−2ζ5−2ζ72ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ7−2ζ13−2ζ232ζ13+2ζ232ζ13+2ζ23−2ζ13−2ζ230000000000000000000000000000000000000000
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χ1064-4-44-4-444-24-4-44-444-4-444-42222-2-2-222-2-2-2-22200000000-222-22-2-2200000000000000000000000000000000000000000000000000000000
χ1074-4-44-4-444-2-444-44-4-44-444-42222-2-2-222-2-2-2-222000000002-2-22-222-200000000000000000000000000000000000000000000000000000000
χ1084-4-44-4-444-2-444-4-444-44-4-442222-2-2-2-2-22222-2-2000000002-2-222-2-2200000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.