Finite Group Databasebeta

← Group #10846318

Character table — Group #10846318

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order12222222344444444666666612121212121212124488888888121212121212121224242424242424242424242424242424224444446666121212121212121212121212244488882244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ9111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-111-1-1-111-1
χ10111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-11-1-1111-1-11
χ11111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-11-111-1-11-1-11
χ12111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-11-11-1-111-111-1
χ13111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111-11-1-1-111-1-111
χ14111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1111-1-111-1-1
χ15111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-11-11-1-1-11111-1-1
χ16111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-1111-1-1-1-111
χ172222222222222-2-2-2-2222222222222222-2-200000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000002-2-2200000000
χ182222222222222-2-2-2-2222222222222222-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-222-200000000
χ19222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-22222-2-2000000000000000000000000000000000000000022-2-200000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-22200000000-2-22222-2-20000000000000000000000000000000000000000-2-22200000000
χ2122222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000
χ2522222222-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-22222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-11111000000000000
χ2622222222-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-22222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-111111111-2-222-2-2221111-1-1-1-11111-1-1-1-1000000000000
χ2722222222-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-2-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-1000000000000
χ2822222222-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-2-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-11111000000000000
χ29222-2-2-22-222i2i−2i−2i2-2-2222-2-22-2-22i2i2i2i−2i−2i−2i−2i2i−2i2i2i−2i−2i22-2-22-22i2i−2i−2i2-22i2i2i2i−2i−2i−2i−2i2222-2-2-2-2000000000000000000000000000000000000
χ30222-2-2-22-222i2i−2i−2i2-2-2222-2-22-2-22i2i2i2i−2i−2i−2i−2i2i−2i−2i−2i2i2i-2-2222-22i2i−2i−2i2-2−2i−2i−2i−2i2i2i2i2i-2-2-2-22222000000000000000000000000000000000000
χ31222-2-2-22-222i2i−2i−2i-222-222-2-22-2-22i2i2i2i−2i−2i−2i−2i−2i2i00000000-22−2i−2i2i2i-22000000000000000000000000000000000000000000002-22i−2i0000
χ32222-2-2-22-222i2i−2i−2i-222-222-2-22-2-22i2i2i2i−2i−2i−2i−2i−2i2i00000000-22−2i−2i2i2i-2200000000000000000000000000000000000000000000-22−2i2i0000
χ33222-2-2-22-22−2i−2i2i2i2-2-2222-2-22-2-2−2i−2i−2i−2i2i2i2i2i−2i2i2i2i−2i−2i-2-2222-2−2i−2i2i2i2-22i2i2i2i−2i−2i−2i−2i-2-2-2-22222000000000000000000000000000000000000
χ34222-2-2-22-22−2i−2i2i2i2-2-2222-2-22-2-2−2i−2i−2i−2i2i2i2i2i−2i2i−2i−2i2i2i22-2-22-2−2i−2i2i2i2-2−2i−2i−2i−2i2i2i2i2i2222-2-2-2-2000000000000000000000000000000000000
χ35222-2-2-22-22−2i−2i2i2i-222-222-2-22-2-2−2i−2i−2i−2i2i2i2i2i2i−2i00000000-222i2i−2i−2i-22000000000000000000000000000000000000000000002-2−2i2i0000
χ36222-2-2-22-22−2i−2i2i2i-222-222-2-22-2-2−2i−2i−2i−2i2i2i2i2i2i−2i00000000-222i2i−2i−2i-2200000000000000000000000000000000000000000000-222i−2i0000
χ37222-2-2-22-2-12i2i−2i−2i2-2-22-1-111-111−i−i−i−iiiii2i−2i2i2i−2i−2i22-2-2-11−i−iii-11−i−i−i−iiiii-1-1-1-1111100000000−i3−i3i3i333−3−333−3−3−i3−i3i3i3000000000000
χ38222-2-2-22-2-12i2i−2i−2i2-2-22-1-111-111−i−i−i−iiiii2i−2i2i2i−2i−2i22-2-2-11−i−iii-11−i−i−i−iiiii-1-1-1-1111100000000i3i3−i3−i3−3−333−3−333i3i3−i3−i3000000000000
χ39222-2-2-22-2-12i2i−2i−2i2-2-22-1-111-111−i−i−i−iiiii2i−2i−2i−2i2i2i-2-222-11−i−iii-11iiii−i−i−i−i1111-1-1-1-100000000−i3−i3i3i333−3−3−3−333i3i3−i3−i3000000000000
χ40222-2-2-22-2-12i2i−2i−2i2-2-22-1-111-111−i−i−i−iiiii2i−2i−2i−2i2i2i-2-222-11−i−iii-11iiii−i−i−i−i1111-1-1-1-100000000i3i3−i3−i3−3−33333−3−3−i3−i3i3i3000000000000
χ41222-2-2-22-2-1−2i−2i2i2i2-2-22-1-111-111iiii−i−i−i−i−2i2i2i2i−2i−2i-2-222-11ii−i−i-11−i−i−i−iiiii1111-1-1-1-100000000−i3−i3i3i3−3−33333−3−3i3i3−i3−i3000000000000
χ42222-2-2-22-2-1−2i−2i2i2i2-2-22-1-111-111iiii−i−i−i−i−2i2i2i2i−2i−2i-2-222-11ii−i−i-11−i−i−i−iiiii1111-1-1-1-100000000i3i3−i3−i333−3−3−3−333−i3−i3i3i3000000000000
χ43222-2-2-22-2-1−2i−2i2i2i2-2-22-1-111-111iiii−i−i−i−i−2i2i−2i−2i2i2i22-2-2-11ii−i−i-11iiii−i−i−i−i-1-1-1-1111100000000−i3−i3i3i3−3−333−3−333−i3−i3i3i3000000000000
χ44222-2-2-22-2-1−2i−2i2i2i2-2-22-1-111-111iiii−i−i−i−i−2i2i−2i−2i2i2i22-2-2-11ii−i−i-11iiii−i−i−i−i-1-1-1-1111100000000i3i3−i3−i333−3−333−3−3i3i3−i3−i3000000000000
χ452-2-222-22-220000-22-22-2-2-2-2222000000000000002-22-2-2-20000220000000022-2-222-2-2002-22-20000002-22-22-22-20000000000000000
χ462-2-222-22-220000-22-22-2-2-2-2222000000000000002-22-2-2-20000220000000022-2-222-2-200-22-22000000-22-22-22-220000000000000000
χ472-2-222-22-220000-22-22-2-2-2-222200000000000000-22-22-2-200002200000000-2-222-2-222002-2-220000002-22-2-22-220000000000000000
χ482-2-222-22-220000-22-22-2-2-2-222200000000000000-22-22-2-200002200000000-2-222-2-22200-222-2000000-22-222-22-20000000000000000
χ492-2-222-22-2-10000-22-221111-1-1-1−i3−i3i3i3−i3−i3i3i30000002-22-211−i3i3−i3i3-1-1−i3−i3i3i3−i3−i3i3i3-1-111-1-111002-22-200−i3i3−i3i3-11-11-11-11−i3i3−i3i3000000000000
χ502-2-222-22-2-10000-22-221111-1-1-1−i3−i3i3i3−i3−i3i3i30000002-22-211−i3i3−i3i3-1-1−i3−i3i3i3−i3−i3i3i3-1-111-1-11100-22-2200i3−i3i3−i31-11-11-11-1i3−i3i3−i3000000000000
χ512-2-222-22-2-10000-22-221111-1-1-1−i3−i3i3i3−i3−i3i3i3000000-22-2211−i3i3−i3i3-1-1i3i3−i3−i3i3i3−i3−i311-1-111-1-1002-2-2200−i3i3−i3i3-11-111-11-1i3−i3i3−i3000000000000
χ522-2-222-22-2-10000-22-221111-1-1-1−i3−i3i3i3−i3−i3i3i3000000-22-2211−i3i3−i3i3-1-1i3i3−i3−i3i3i3−i3−i311-1-111-1-100-222-200i3−i3i3−i31-11-1-11-11−i3i3−i3i3000000000000
χ532-2-222-22-2-10000-22-221111-1-1-1i3i3−i3−i3i3i3−i3−i30000002-22-211i3−i3i3−i3-1-1i3i3−i3−i3i3i3−i3−i3-1-111-1-111002-22-200i3−i3i3−i3-11-11-11-11i3−i3i3−i3000000000000
χ542-2-222-22-2-10000-22-221111-1-1-1i3i3−i3−i3i3i3−i3−i30000002-22-211i3−i3i3−i3-1-1i3i3−i3−i3i3i3−i3−i3-1-111-1-11100-22-2200−i3i3−i3i31-11-11-11-1−i3i3−i3i3000000000000
χ552-2-222-22-2-10000-22-221111-1-1-1i3i3−i3−i3i3i3−i3−i3000000-22-2211i3−i3i3−i3-1-1−i3−i3i3i3−i3−i3i3i311-1-111-1-1002-2-2200i3−i3i3−i3-11-111-11-1−i3i3−i3i3000000000000
χ562-2-222-22-2-10000-22-221111-1-1-1i3i3−i3−i3i3i3−i3−i3000000-22-2211i3−i3i3−i3-1-1−i3−i3i3i3−i3−i3i3i311-1-111-1-100-222-200−i3i3−i3i31-11-1-11-11i3−i3i3−i3000000000000
χ572-2-2-2-222220000-2-222-2-2222-2-2000000000000002-2-22-2200002-20000000022-2-2-2-2222-200002-22-2-22000000002-2-22000000000000
χ582-2-2-2-222220000-2-222-2-2222-2-2000000000000002-2-22-2200002-20000000022-2-2-2-222-220000-22-222-200000000-222-2000000000000
χ592-2-2-2-222220000-2-222-2-2222-2-200000000000000-222-2-2200002-200000000-2-22222-2-22-20000-222-2-2200000000-222-2000000000000
χ602-2-2-2-222220000-2-222-2-2222-2-200000000000000-222-2-2200002-200000000-2-22222-2-2-2200002-2-222-2000000002-2-22000000000000
χ612-2-2-2-2222-10000-2-22211-1-1-11133−3−3−3−3330000002-2-221-13−3−33-1133−3−3−3−333-1-11111-1-12-200002-2-111-13−3−333−3−33-111-1000000000000
χ622-2-2-2-2222-10000-2-22211-1-1-11133−3−3−3−3330000002-2-221-13−3−33-1133−3−3−3−333-1-11111-1-1-220000-221-1-11−333−3−333−31-1-11000000000000
χ632-2-2-2-2222-10000-2-22211-1-1-11133−3−3−3−333000000-222-21-13−3−33-11−3−33333−3−311-1-1-1-1112-20000-22-111-13−3−33−333−31-1-11000000000000
χ642-2-2-2-2222-10000-2-22211-1-1-11133−3−3−3−333000000-222-21-13−3−33-11−3−33333−3−311-1-1-1-111-2200002-21-1-11−333−33−3−33-111-1000000000000
χ652-2-2-2-2222-10000-2-22211-1-1-111−3−33333−3−30000002-2-221-1−333−3-11−3−33333−3−3-1-11111-1-12-200002-2-111-1−333−3−333−3-111-1000000000000
χ662-2-2-2-2222-10000-2-22211-1-1-111−3−33333−3−30000002-2-221-1−333−3-11−3−33333−3−3-1-11111-1-1-220000-221-1-113−3−333−3−331-1-11000000000000
χ672-2-2-2-2222-10000-2-22211-1-1-111−3−33333−3−3000000-222-21-1−333−3-1133−3−3−3−33311-1-1-1-1112-20000-22-111-1−333−33−3−331-1-11000000000000
χ682-2-2-2-2222-10000-2-22211-1-1-111−3−33333−3−3000000-222-21-1−333−3-1133−3−3−3−33311-1-1-1-111-2200002-21-1-113−3−33−333−3-111-1000000000000
χ6944444444-24444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-4-400000000222222220000000000000000000000000000000000000000000000000000
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χ72444-4-4-44-4-2−4i−4i4i4i-444-4-2-222-2222i2i2i2i−2i−2i−2i−2i4i−4i000000002-2−2i−2i2i2i2-20000000000000000000000000000000000000000000000000000
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χ864-444-4-4-444-44-440000-44-44-44-4-444-4-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ874-444-4-4-44-24-44-400002-22-22-22-222-2-222-20000000000000000006−6−666−6−66−666−6−666−6000000000000000000000000000000000000
χ884-444-4-4-44-24-44-400002-22-22-22-222-2-222-2000000000000000000−666−6−666−66−6−666−6−66000000000000000000000000000000000000
χ894-444-4-4-44-2-44-4400002-22-22-222-2-222-2-220000000000000000006−6−666−6−666−6−666−6−66000000000000000000000000000000000000
χ904-444-4-4-44-2-44-4400002-22-22-222-2-222-2-22000000000000000000−666−6−666−6−666−6−666−6000000000000000000000000000000000000
χ914-44-444-4-444i−4i−4i4i0000-444-4-4-444i−4i−4i4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000
χ924-44-444-4-44−4i4i4i−4i0000-444-4-4-44−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000
χ934-44-444-4-4-24i−4i−4i4i00002-2-2222-2−2i2i2i−2i2i−2i−2i2i000000000000000000i6−i6−i6i6−i6i6i6−i6−666−66−6−66000000000000000000000000000000000000
χ944-44-444-4-4-24i−4i−4i4i00002-2-2222-2−2i2i2i−2i2i−2i−2i2i000000000000000000−i6i6i6−i6i6−i6−i6i66−6−66−666−6000000000000000000000000000000000000
χ954-44-444-4-4-2−4i4i4i−4i00002-2-2222-22i−2i−2i2i−2i2i2i−2i000000000000000000i6−i6−i6i6−i6i6i6−i66−6−66−666−6000000000000000000000000000000000000
χ964-44-444-4-4-2−4i4i4i−4i00002-2-2222-22i−2i−2i2i−2i2i2i−2i000000000000000000−i6i6i6−i6i6−i6−i6i6−666−66−6−66000000000000000000000000000000000000
χ974-4-444-44-4400004-44-4-4-4-4-4444000000000000000000440000-4-40000000000000000000000000000000000000000000000000000
χ984-4-444-44-4-200004-44-42222-2-2-2−2i3−2i32i32i3−2i3−2i32i32i30000000000-2-22i3−2i32i3−2i3220000000000000000000000000000000000000000000000000000
χ994-4-444-44-4-200004-44-42222-2-2-22i32i3−2i3−2i32i32i3−2i3−2i30000000000-2-2−2i32i3−2i32i3220000000000000000000000000000000000000000000000000000
χ1004-4-4-4-44444000044-4-4-4-4444-4-40000000000000000004-40000-440000000000000000000000000000000000000000000000000000
χ1014-4-4-4-4444-2000044-4-422-2-2-2222323−23−23−23−2323230000000000-22−232323−232-20000000000000000000000000000000000000000000000000000
χ1024-4-4-4-4444-2000044-4-422-2-2-222−23−2323232323−23−230000000000-2223−23−23232-20000000000000000000000000000000000000000000000000000

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