Finite Group Databasebeta

← Group #10693679

Character table — Group #10693679

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order12224444344444444666121212122466888888881212121212121212121224242424242424242424242424242424448812121212242424248888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-11-1-11111-1-1111-1-1-1-1-11-1-1iiii−i−i−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1i−i11-1-1ii−i−ii−ii−i11-1-1ii−i−i11-1-1
χ101111-1-1-1-11-1-11111-1-1111-1-1-1-1-11-1-1iiii−i−i−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1i−i11-1-1ii−i−i−ii−ii-1-111−i−iii-1-111
χ111111-1-1-1-11-1-11111-1-1111-1-1-1-1-11-1-1iiii−i−i−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11−ii-1-111−i−iiii−ii−i11-1-1−i−iii-1-111
χ121111-1-1-1-11-1-11111-1-1111-1-1-1-1-11-1-1iiii−i−i−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11−ii-1-111−i−iii−ii−ii-1-111ii−i−i11-1-1
χ131111-1-1-1-11-1-11111-1-1111-1-1-1-1-11-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1−ii11-1-1−i−iiii−ii−i-1-111ii−i−i-1-111
χ141111-1-1-1-11-1-11111-1-1111-1-1-1-1-11-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1−ii11-1-1−i−iii−ii−ii11-1-1−i−iii11-1-1
χ151111-1-1-1-11-1-11111-1-1111-1-1-1-1-11-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11i−i-1-111ii−i−ii−ii−i-1-111−i−iii11-1-1
χ161111-1-1-1-11-1-11111-1-1111-1-1-1-1-11-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11i−i-1-111ii−i−i−ii−ii11-1-1ii−i−i-1-111
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χ19222222222-2-2-2-222222222222-2-2-2-200000000-2-2-2-22222-2-2000000000000000000000000000022-2-2000000000000
χ20222222222-2-2-2-222222222222-2-2-2-200000000-2-2-2-22222-2-20000000000000000000000000000-2-222000000000000
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χ2322222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
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χ2522222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-111110000000000000000
χ2622222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-10000000000000000
χ2722222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-21122-2-222-2-211-1-11111-1-1-1-1-1-11111-1-1-1-111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2822222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-21122-2-222-2-211-1-11111-1-1-1-1-1-11111-1-1-1-111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2922222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-211-2-222-2-22211-1-11111-1-11111-1-1-1-11111-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ3022222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-211-2-222-2-22211-1-11111-1-11111-1-1-1-11111-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
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χ382222-2-2-2-2-1-2-22222-2-2-1-1-11111-22112i2i2i2i−2i−2i−2i−2i-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-22−2i2i11-1-1ii−i−i0000000000000000
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χ402222-2-2-2-2-1-2-22222-2-2-1-1-11111-2211−2i−2i−2i−2i2i2i2i2i-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-222i−2i11-1-1−i−iii0000000000000000
χ412222-2-2-2-2-1-2-222-2-222-1-1-111112-2-1-12i2i−2i−2i−2i−2i2i2i11-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i0000−i3i3i3−i33−3−330000000000000000
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χ432222-2-2-2-2-1-2-222-2-222-1-1-111112-2-1-1−2i−2i2i2i2i2i−2i−2i11-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii0000−i3i3i3−i3−333−30000000000000000
χ442222-2-2-2-2-1-2-222-2-222-1-1-111112-2-1-1−2i−2i2i2i2i2i−2i−2i11-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii0000i3−i3−i3i33−3−330000000000000000
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χ462-22-22i−2i2i−2i22i−2i2-20000-22-22i−2i2i−2i000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23002-200002i−2i0000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ2300000000000000000000−1−i1+i−1+i1−ii2−i2−22
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χ5344444444-2-4-4-4-44444-2-2-2-2-2-2-2-4-422000000002222-2-2-2-22200000000000000000000000000000000000000000000
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χ824-4-444i−4i−4i4i-200004-44i−4i22-2−2i2i2i−2i0000000000000000-22−2i2i00ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000000000000000000
χ834-4-444i−4i−4i4i-20000-44−4i4i22-2−2i2i2i−2i00000000000000002-22i−2i00−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ220000000000000000000000000000
χ844-4-444i−4i−4i4i-20000-44−4i4i22-2−2i2i2i−2i00000000000000002-22i−2i00ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ220000000000000000000000000000
χ854-4-44−4i4i4i−4i400004-4−4i4i-4-44−4i4i4i−4i00000000000000004-4−4i4i0000000000000000000000000000000000000000000000
χ864-4-44−4i4i4i−4i40000-444i−4i-4-44−4i4i4i−4i0000000000000000-444i−4i0000000000000000000000000000000000000000000000
χ874-4-44−4i4i4i−4i-200004-4−4i4i22-22i−2i−2i2i0000000000000000-222i−2i00−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000000000000000000
χ884-4-44−4i4i4i−4i-200004-4−4i4i22-22i−2i−2i2i0000000000000000-222i−2i00ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000000000000000000
χ894-4-44−4i4i4i−4i-20000-444i−4i22-22i−2i−2i2i00000000000000002-2−2i2i00−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ220000000000000000000000000000
χ904-4-44−4i4i4i−4i-20000-444i−4i22-22i−2i−2i2i00000000000000002-2−2i2i00ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ220000000000000000000000000000

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