Finite Group Databasebeta

← Group #10690025

Character table — Group #10690025

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222444444444444444444444444444444444488888888888888888888888888121212121212121224242424242424244848
order12222222344444444666666644444444441212121212121212121212121212121212121212121212122244444466661212121212121212121212121212888888888888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ91-11-1-11-11111-11-1-1-11-111-1-11-11ii−i−i11-1-1-111-1-1iiii−i−i−i−i11-1-11111-1-1-1-11-1i−iii−i−i11-1-11-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i1-1
χ101-11-1-11-11111-11-1-1-11-111-1-11-11ii−i−i11-1-1-111-1-1iiii−i−i−i−i11-1-11111-1-1-1-11-1i−iii−i−i11-1-11-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111−i−iii-11
χ111-11-1-11-11111-11-1-1-11-111-1-11-11ii−i−i-1-111-111-1-1iiii−i−i−i−i11-1-1-1-1-1-11111-11i−i−i−iii-1-1111-1ii−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iii-11
χ121-11-1-11-11111-11-1-1-11-111-1-11-11ii−i−i-1-111-111-1-1iiii−i−i−i−i11-1-1-1-1-1-11111-11i−i−i−iii-1-1111-1ii−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−i1-1
χ131-11-1-11-11111-11-1-1-11-111-1-11-11−i−iii11-1-1-111-1-1−i−i−i−iiiii11-1-11111-1-1-1-11-1−ii−i−iii11-1-11-1−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i-11
χ141-11-1-11-11111-11-1-1-11-111-1-11-11−i−iii11-1-1-111-1-1−i−i−i−iiiii11-1-11111-1-1-1-11-1−ii−i−iii11-1-11-1−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii1-1
χ151-11-1-11-11111-11-1-1-11-111-1-11-11−i−iii-1-111-111-1-1−i−i−i−iiiii11-1-1-1-1-1-11111-11−iiii−i−i-1-1111-1−i−iiiiiii−i−i−i−iiiii−i−i−i−i-1-111−i−iii1-1
χ161-11-1-11-11111-11-1-1-11-111-1-11-11−i−iii-1-111-111-1-1−i−i−i−iiiii11-1-1-1-1-1-11111-11−iiii−i−i-1-1111-1−i−iiiiiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i-11
χ17222222222222-2-2-22-22222222-222220000-2-2-2-2-22222222222220000000000-2-200000000-2-2-2-2-2-200000000000000000000000000
χ18222222222222-2-2-22-22222222-2-2-2-2-20000-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000002200000000-2-2222200000000000000000000000000
χ19222222222-2-2-2222-222222222-200002222-2222200000000-2-2-2-222222222-2-2000000-2-2-2-2-2-2000000000000000000000000000000
χ20222222222-2-2-2222-222222222-20000-2-2-2-2-2222200000000-2-2-2-2-2-2-2-2-2-2-2-2220000002222-2-2000000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-222222222000000002-2-2-2-200000000-2-2-2-20000000000002-22-2000022000022-2-222-2-2000000000000000000
χ22222222222-2-2-2-2-2-2-2-222222222000000002-2-2-2-200000000-2-2-2-2000000000000-22-220000220000-2-222-2-222000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ2422222222-122222222-1-1-1-1-1-1-122222-2-2-2-22-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-222-2-2-2-21111-1-1-1-1-1-111111111000000000000000000
χ2522222222-122222222-1-1-1-1-1-1-12-2-2-2-222222-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-1-1-1-1-1-1111111111111000000000000000000
χ2622222222-122222222-1-1-1-1-1-1-12-2-2-2-2-2-2-2-22-1-1-1-111111111-1-1-1-111111111-2-2-2-222221111-1-11111-1-1-1-1-1-1-1-1000000000000000000
χ2722222222-1222-2-2-22-2-1-1-1-1-1-1-1-222220000-21111-1-1-1-1-1-1-1-1-1-1-1-1−i3−i3i3i3−i3−i3i3i300-2-20000−i3i3−i3i3111111−i3i3−i3i3−i3i3−i3i3000000000000000000
χ2822222222-1222-2-2-22-2-1-1-1-1-1-1-1-222220000-21111-1-1-1-1-1-1-1-1-1-1-1-1i3i3−i3−i3i3i3−i3−i300-2-20000i3−i3i3−i3111111i3−i3i3−i3i3−i3i3−i3000000000000000000
χ2922222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-2-2-20000-2111111111111-1-1-1-1−i3−i3i3i3−i3−i3i3i300220000−i3i3−i3i311-1-1-1-1i3−i3i3−i3i3−i3i3−i3000000000000000000
χ3022222222-1222-2-2-22-2-1-1-1-1-1-1-1-2-2-2-2-20000-2111111111111-1-1-1-1i3i3−i3−i3i3i3−i3−i300220000i3−i3i3−i311-1-1-1-1−i3i3−i3i3−i3i3−i3i3000000000000000000
χ3122222222-1-2-2-2222-22-1-1-1-1-1-1-1-200002222-2-1-1-1-1−i3−i3i3i3−i3−i3i3i31111-1-1-1-1-1-1-1-1-2-2000000111111−i3i3−i3i3−i3i3i3−i3−i3i3i3−i3000000000000000000
χ3222222222-1-2-2-2222-22-1-1-1-1-1-1-1-200002222-2-1-1-1-1i3i3−i3−i3i3i3−i3−i31111-1-1-1-1-1-1-1-1-2-2000000111111i3−i3i3−i3i3−i3−i3i3i3−i3−i3i3000000000000000000
χ3322222222-1-2-2-2222-22-1-1-1-1-1-1-1-20000-2-2-2-2-2-1-1-1-1−i3−i3i3i3−i3−i3i3i311111111111122000000-1-1-1-111−i3i3−i3i3i3−i3−i3i3i3−i3−i3i3000000000000000000
χ3422222222-1-2-2-2222-22-1-1-1-1-1-1-1-20000-2-2-2-2-2-1-1-1-1i3i3−i3−i3i3i3−i3−i311111111111122000000-1-1-1-111i3−i3i3−i3−i3i3i3−i3−i3i3i3−i3000000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-120000000021111−i3−i3i3i3−i3−i3i3i31111−i3−i3i3i3−i3−i3i3i300002-22-2i3−i3i3−i3-1-1i3−i3i3−i3-1-111-1-111000000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-120000000021111−i3−i3i3i3−i3−i3i3i31111i3i3−i3−i3i3i3−i3−i30000-22-22−i3i3−i3i3-1-1i3−i3i3−i311-1-111-1-1000000000000000000
χ3722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-120000000021111i3i3−i3−i3i3i3−i3−i31111−i3−i3i3i3−i3−i3i3i30000-22-22i3−i3i3−i3-1-1−i3i3−i3i311-1-111-1-1000000000000000000
χ3822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-120000000021111i3i3−i3−i3i3i3−i3−i31111i3i3−i3−i3i3i3−i3−i300002-22-2−i3i3−i3i3-1-1−i3i3−i3i3-1-111-1-111000000000000000000
χ3922-22-22-2-222-2-2000202-2-22-22-202i−2i2i−2i0000000002i−2i2i−2i2i−2i2i−2i2-22-2000000000000000000000000000000000022−2−222−2−2−i2i2−i2i2000000
χ4022-22-22-2-222-2-2000202-2-22-22-202i−2i2i−2i0000000002i−2i2i−2i2i−2i2i−2i2-22-20000000000000000000000000000000000−2−222−2−222i2−i2i2−i2000000
χ4122-22-22-2-222-2-2000202-2-22-22-20−2i2i−2i2i000000000−2i2i−2i2i−2i2i−2i2i2-22-2000000000000000000000000000000000022−2−222−2−2i2−i2i2−i2000000
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χ4322-2-2-2-222200022-20-222-2-2-2-22000002i−2i2i−2i02-22-20000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000002−22−22−22−20000−i2i2−i2i200
χ4422-2-2-2-222200022-20-222-2-2-2-22000002i−2i2i−2i02-22-20000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000−22−22−22−220000i2−i2i2−i200
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χ472-22-2-22-22222-2-222-2-2-222-2-22-2-22i2i−2i−2i00002-2-2222i2i2i2i−2i−2i−2i−2i22-2-20000000000−2i2i00000000-22−2i−2i2i2i00000000000000000000000000
χ482-22-2-22-22222-2-222-2-2-222-2-22-2-2−2i−2i2i2i00002-2-222−2i−2i−2i−2i2i2i2i2i22-2-200000000002i−2i00000000-222i2i−2i−2i00000000000000000000000000
χ492-22-2-22-222-2-222-2-222-222-2-22-2-2000022-2-2222-2-200000000-2-2222222-2-2-2-2-22000000-2-222-22000000000000000000000000000000
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χ522-22-2-22-222-2-22-2222-2-222-2-22-2200000000-2-2-22200000000-2-222000000000000−2i2i2i−2i00002-20000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ532-22-2-22-22-122-22-2-2-221-1-111-1122i2i−2i−2i22-2-2-2-1-111−i−i−i−iiiii-1-111-1-1-1-111112-22i−2i2i2i−2i−2i-1-111-11−i−iii−i−i−i−iiiii000000000000000000
χ542-22-2-22-22-122-22-2-2-221-1-111-1122i2i−2i−2i-2-222-2-1-111−i−i−i−iiiii-1-1111111-1-1-1-1-222i−2i−2i−2i2i2i11-1-1-11−i−iiiiiii−i−i−i−i000000000000000000
χ552-22-2-22-22-122-22-2-2-221-1-111-112−2i−2i2i2i22-2-2-2-1-111iiii−i−i−i−i-1-111-1-1-1-111112-2−2i2i−2i−2i2i2i-1-111-11ii−i−iiiii−i−i−i−i000000000000000000
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χ572-22-2-22-22-122-2-222-2-21-1-111-11-22i2i−2i−2i0000211-1-1−i−i−i−iiiii-1-111−i3−i3i3i3i3i3−i3−i300−2i2i0000−i3i3i3−i31-1ii−i−i3−33−3−33−33000000000000000000
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χ592-22-2-22-22-122-2-222-2-21-1-111-11-2−2i−2i2i2i0000211-1-1iiii−i−i−i−i-1-111−i3−i3i3i3i3i3−i3−i3002i−2i0000−i3i3i3−i31-1−i−iii−33−333−33−3000000000000000000
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χ642-22-2-22-22-1-2-222-2-2221-1-111-11-20000-2-2222-1-111−3−33333−3−311-1-11111-1-1-1-12-2000000-1-1111-1−333−33−3−33−333−3000000000000000000
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χ8644-4-4-4-444-200044-40-4-2-22222-200000−4i4i−4i4i0-22-220000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000
χ8744-4-4-4-444-2000-4-4404-2-22222-200000000002-22-200000000000023−23−232323−23−232300000000000000000000000000000000000000000000
χ8844-4-4-4-444-2000-4-4404-2-22222-200000000002-22-2000000000000−232323−23−232323−2300000000000000000000000000000000000000000000
χ894-444-4-44-4400000000-4-444-4-440000000000000000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ904-444-4-44-4400000000-4-444-4-44000000000000000000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ914-4-444-4-444000-44-404-44-444-4-40000000000-444-40000000000000000000000000000000000000000000000000000000000000000
χ924-4-444-4-44-20004-440-42-22-2-222000004i−4i−4i4i0-222-2000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000000000
χ934-4-444-4-44-20004-440-42-22-2-22200000−4i4i4i−4i0-222-20000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000000000000
χ944-4-444-4-44-2000-44-4042-22-2-22200000000002-2-2200000000000023−23−2323−232323−2300000000000000000000000000000000000000000000
χ954-4-444-4-44-2000-44-4042-22-2-22200000000002-2-22000000000000−232323−2323−23−232300000000000000000000000000000000000000000000
χ964-4-4-4444-44-44-400040-4-4-4-44440000000000000000000000-444-40000000000000000000000000000000000000000000000000000
χ974-4-4-4444-4-24-44000-402222-2-2-204-4-44000000000-22-222-22-2-222-20000000000000000000000000000000000000000000000000000
χ984-4-4-4444-4-24-44000-402222-2-2-20-444-40000000002-22-2-22-22-222-20000000000000000000000000000000000000000000000000000
χ994-4-4-4444-4-2-44-4000402222-2-2-200000000000000−2i32i32i3−2i32i3−2i3−2i32i32-2-220000000000000000000000000000000000000000000000000000
χ1004-4-4-4444-4-2-44-4000402222-2-2-2000000000000002i3−2i3−2i32i3−2i32i32i3−2i32-2-220000000000000000000000000000000000000000000000000000
χ101888-88-8-8-8-400000000-44-44-444000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-888-8-88-8-40000000044-4-444-4000000000000000000000000000000000000000000000000000000000000000000000000000000

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