Finite Group Databasebeta

← Group #10845387

Character table — Group #10845387

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222222224444444444444444444444444444444444888888888888888888888888242424242424242448484848
order122222223444444446666666121212121212121244888888881212121212121212242424242424242424242424242424244444444412121212121212121212121212121212224488884444
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
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11-11-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-11-11
χ9111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1
χ10111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111
χ11111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-11-111-1-1-1-111
χ12111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-11-11-1-11111-1-1
χ13111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111-11-1-1-111-111-1
χ14111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1111-1-11-1-11
χ15111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-11-11-1-1-1111-1-11
χ16111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-1111-1-1-111-1
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
χ29222-2-2-22-2200002-2-222-2-22-22-20000000000000022-2-22-200002-2000000002222-2-2-2-2002i−2i2i−2i0000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ30222-2-2-22-2200002-2-222-2-22-22-20000000000000022-2-22-200002-2000000002222-2-2-2-200−2i2i−2i2i000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ31222-2-2-22-2200002-2-222-2-22-22-200000000000000-2-2222-200002-200000000-2-2-2-22222002i−2i−2i2i0000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ32222-2-2-22-2200002-2-222-2-22-22-200000000000000-2-2222-200002-200000000-2-2-2-2222200−2i2i2i−2i000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ33222-2-2-22-2-100002-2-22-111-11-113333−3−3−3−300000022-2-2-1133−3−3-113333−3−3−3−3-1-1-1-11111002i−2i2i−2i00−i3−i3i3i3−i−iii−i−iii−i3−i3i3i3000000000000
χ34222-2-2-22-2-100002-2-22-111-11-113333−3−3−3−300000022-2-2-1133−3−3-113333−3−3−3−3-1-1-1-1111100−2i2i−2i2i00i3i3−i3−i3ii−i−iii−i−ii3i3−i3−i3000000000000
χ35222-2-2-22-2-100002-2-22-111-11-113333−3−3−3−3000000-2-222-1133−3−3-11−3−3−3−333331111-1-1-1-1002i−2i−2i2i00−i3−i3i3i3−i−iiiii−i−ii3i3−i3−i3000000000000
χ36222-2-2-22-2-100002-2-22-111-11-113333−3−3−3−3000000-2-222-1133−3−3-11−3−3−3−333331111-1-1-1-100−2i2i2i−2i00i3i3−i3−i3ii−i−i−i−iii−i3−i3i3i3000000000000
χ37222-2-2-22-2-100002-2-22-111-11-11−3−3−3−3333300000022-2-2-11−3−333-11−3−3−3−33333-1-1-1-11111002i−2i2i−2i00i3i3−i3−i3−i−iii−i−iiii3i3−i3−i3000000000000
χ38222-2-2-22-2-100002-2-22-111-11-11−3−3−3−3333300000022-2-2-11−3−333-11−3−3−3−33333-1-1-1-1111100−2i2i−2i2i00−i3−i3i3i3ii−i−iii−i−i−i3−i3i3i3000000000000
χ39222-2-2-22-2-100002-2-22-111-11-11−3−3−3−33333000000-2-222-11−3−333-113333−3−3−3−31111-1-1-1-1002i−2i−2i2i00i3i3−i3−i3−i−iiiii−i−i−i3−i3i3i3000000000000
χ40222-2-2-22-2-100002-2-22-111-11-11−3−3−3−33333000000-2-222-11−3−333-113333−3−3−3−31111-1-1-1-100−2i2i2i−2i00−i3−i3i3i3ii−i−i−i−iiii3i3−i3−i3000000000000
χ412-2-22-222-2200002-22-2-22-2-222-2000000000000002i−2i2i−2i2-20000-22000000002i2i−2i−2i2i2i−2i−2i2i−2i00002-22i−2i2i−2i000000002-22-2000000000000
χ422-2-22-222-2200002-22-2-22-2-222-2000000000000002i−2i2i−2i2-20000-22000000002i2i−2i−2i2i2i−2i−2i−2i2i0000-22−2i2i−2i2i00000000-22-22000000000000
χ432-2-22-222-2200002-22-2-22-2-222-200000000000000−2i2i−2i2i2-20000-2200000000−2i−2i2i2i−2i−2i2i2i2i−2i0000-222i−2i2i−2i00000000-22-22000000000000
χ442-2-22-222-2200002-22-2-22-2-222-200000000000000−2i2i−2i2i2-20000-2200000000−2i−2i2i2i−2i−2i2i2i−2i2i00002-2−2i2i−2i2i000000002-22-2000000000000
χ452-2-22-222-2-100002-22-21-111-1-1133−3−333−3−30000002i−2i2i−2i-113−33−31-1−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii2i−2i00002-2−ii−ii−i3i3−i3i33−33−3-11-11000000000000
χ462-2-22-222-2-100002-22-21-111-1-1133−3−333−3−30000002i−2i2i−2i-113−33−31-1−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii−2i2i0000-22i−ii−ii3−i3i3−i3−33−331-11-1000000000000
χ472-2-22-222-2-100002-22-21-111-1-1133−3−333−3−3000000−2i2i−2i2i-113−33−31-1i3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i2i−2i0000-22−ii−ii−i3i3−i3i3−33−331-11-1000000000000
χ482-2-22-222-2-100002-22-21-111-1-1133−3−333−3−3000000−2i2i−2i2i-113−33−31-1i3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i−2i2i00002-2i−ii−ii3−i3i3−i33−33−3-11-11000000000000
χ492-2-22-222-2-100002-22-21-111-1-11−3−333−3−3330000002i−2i2i−2i-11−33−331-1i3i3−i3−i3i3i3−i3−i3−i−iii−i−iii2i−2i00002-2−ii−iii3−i3i3−i3−33−33-11-11000000000000
χ502-2-22-222-2-100002-22-21-111-1-11−3−333−3−3330000002i−2i2i−2i-11−33−331-1i3i3−i3−i3i3i3−i3−i3−i−iii−i−iii−2i2i0000-22i−ii−i−i3i3−i3i33−33−31-11-1000000000000
χ512-2-22-222-2-100002-22-21-111-1-11−3−333−3−333000000−2i2i−2i2i-11−33−331-1−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i2i−2i0000-22−ii−iii3−i3i3−i33−33−31-11-1000000000000
χ522-2-22-222-2-100002-22-21-111-1-11−3−333−3−333000000−2i2i−2i2i-11−33−331-1−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i−2i2i00002-2i−ii−i−i3i3−i3i3−33−33-11-11000000000000
χ532-2-2-22-222222-2-222-2-2-2-22-2-22222-2-2-2-2222-22i2i−2i−2i2i−2i−2i2i222-2-22-2-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ542-2-2-22-222222-2-222-2-2-2-22-2-22222-2-2-2-2222-2−2i−2i2i2i−2i2i2i−2i222-2-22-2-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ552-2-2-22-222222-2-2-2-222-2-22-2-22222-2-2-2-222-2200000000-2-2-222-222000000000000000000000000000000000000000000002-22-20000
χ562-2-2-22-222222-2-2-2-222-2-22-2-22222-2-2-2-222-2200000000-2-2-222-22200000000000000000000000000000000000000000000-22-220000
χ572-2-2-22-2222-2-22222-2-2-2-22-2-222-2-22222-2-2-222i2i−2i−2i−2i2i2i−2i22-222-2-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ582-2-2-22-2222-2-22222-2-2-2-22-2-222-2-22222-2-2-22−2i−2i2i2i2i−2i−2i2i22-222-2-2-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ592-2-2-22-2222-2-222-2-222-2-22-2-222-2-22222-2-22-200000000-2-22-2-2222000000000000000000000000000000000000000000002-2-220000
χ602-2-2-22-2222-2-222-2-222-2-22-2-222-2-22222-2-22-200000000-2-22-2-222200000000000000000000000000000000000000000000-222-20000
χ612-2-2-22-222-122-2-222-2-211-111-1-1-1-11111-1-12-22i2i−2i−2i2i−2i−2i2i-1-1-111-111ii−i−i−i−iii−i−iiiii−i−i000000003−3−33−333−3−i3i3i3−i3−i3i3i3−i3000000000000
χ622-2-2-22-222-122-2-222-2-211-111-1-1-1-11111-1-12-22i2i−2i−2i2i−2i−2i2i-1-1-111-111ii−i−i−i−iii−i−iiiii−i−i00000000−333−33−3−33i3−i3−i3i3i3−i3−i3i3000000000000
χ632-2-2-22-222-122-2-222-2-211-111-1-1-1-11111-1-12-2−2i−2i2i2i−2i2i2i−2i-1-1-111-111−i−iiiii−i−iii−i−i−i−iii000000003−3−33−333−3i3−i3−i3i3i3−i3−i3i3000000000000
χ642-2-2-22-222-122-2-222-2-211-111-1-1-1-11111-1-12-2−2i−2i2i2i−2i2i2i−2i-1-1-111-111−i−iiiii−i−iii−i−i−i−iii00000000−333−33−3−33−i3i3i3−i3−i3i3i3−i3000000000000
χ652-2-2-22-222-1-2-22222-2-211-111-1-111-1-1-1-111-222i2i−2i−2i−2i2i2i−2i-1-11-1-1111ii−i−i−i−iiiii−i−i−i−iii000000003−3−333−3−33−i3i3i3−i3i3−i3−i3i3000000000000
χ662-2-2-22-222-1-2-22222-2-211-111-1-111-1-1-1-111-222i2i−2i−2i−2i2i2i−2i-1-11-1-1111ii−i−i−i−iiiii−i−i−i−iii00000000−333−3−333−3i3−i3−i3i3−i3i3i3−i3000000000000
χ672-2-2-22-222-1-2-22222-2-211-111-1-111-1-1-1-111-22−2i−2i2i2i2i−2i−2i2i-1-11-1-1111−i−iiiii−i−i−i−iiiii−i−i000000003−3−333−3−33i3−i3−i3i3−i3i3i3−i3000000000000
χ682-2-2-22-222-1-2-22222-2-211-111-1-111-1-1-1-111-22−2i−2i2i2i2i−2i−2i2i-1-11-1-1111−i−iiiii−i−i−i−iiiii−i−i00000000−333−3−333−3−i3i3i3−i3i3−i3−i3i3000000000000
χ6944444444-24444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-4-400000000222222220000000000000000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-222222222440000000022-2-2-2-2220000000000000000000000000000000000000000000000000000
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χ7744-444-4-4-4-200000000-2-2-22222−2i32i3−2i32i3−2i32i3−2i32i300−2222−22220000000000002−22−22−22−2−i6i6−i6i6−i6i6−i6i6000000000000000000000000000000000000
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χ7944-444-4-4-4-200000000-2-2-222222i3−2i32i3−2i32i3−2i32i3−2i300−2222−22220000000000002−22−22−22−2i6−i6i6−i6i6−i6i6−i6000000000000000000000000000000000000
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χ864-444-4-4-4444i−4i−4i4i0000-44-44-4-444i−4i−4i4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000
χ874-444-4-4-444−4i4i4i−4i0000-44-44-4-44−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000
χ884-444-4-4-44-24i−4i−4i4i00002-22-222-2−2i2i2i−2i−2i2i2i−2i000000000000000000i6−i6−i6i6i6−i6−i6i66−6−666−6−66000000000000000000000000000000000000
χ894-444-4-4-44-24i−4i−4i4i00002-22-222-2−2i2i2i−2i−2i2i2i−2i000000000000000000−i6i6i6−i6−i6i6i6−i6−666−6−666−6000000000000000000000000000000000000
χ904-444-4-4-44-2−4i4i4i−4i00002-22-222-22i−2i−2i2i2i−2i−2i2i000000000000000000i6−i6−i6i6i6−i6−i6i6−666−6−666−6000000000000000000000000000000000000
χ914-444-4-4-44-2−4i4i4i−4i00002-22-222-22i−2i−2i2i2i−2i−2i2i000000000000000000−i6i6i6−i6−i6i6i6−i66−6−666−6−66000000000000000000000000000000000000
χ924-44-444-4-4400000000-4-4444-4-40000000000−2i22i22i2−2i20000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000000000
χ934-44-444-4-4400000000-4-4444-4-400000000002i2−2i2−2i22i2000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000000000
χ944-44-444-4-4-20000000022-2-2-222−2i32i32i3−2i32i3−2i3−2i32i300−2i22i22i2−2i2000000000000−i2i2i2−i2i2−i2−i2i26−6−66−666−6000000000000000000000000000000000000
χ954-44-444-4-4-20000000022-2-2-222−2i32i32i3−2i32i3−2i3−2i32i3002i2−2i2−2i22i2000000000000i2−i2−i2i2−i2i2i2−i2−666−66−6−66000000000000000000000000000000000000
χ964-44-444-4-4-20000000022-2-2-2222i3−2i3−2i32i3−2i32i32i3−2i300−2i22i22i2−2i2000000000000−i2i2i2−i2i2−i2−i2i2−666−66−6−66000000000000000000000000000000000000
χ974-44-444-4-4-20000000022-2-2-2222i3−2i3−2i32i3−2i32i32i3−2i3002i2−2i2−2i22i2000000000000i2−i2−i2i2−i2i2i2−i26−6−66−666−6000000000000000000000000000000000000
χ984-4-44-444-440000-44-44-44-4-444-4000000000000000000-4400004-40000000000000000000000000000000000000000000000000000
χ994-4-44-444-4-20000-44-442-222-2-222323−23−232323−23−2300000000002-2−2323−2323-220000000000000000000000000000000000000000000000000000
χ1004-4-44-444-4-20000-44-442-222-2-22−23−232323−23−23232300000000002-223−2323−23-220000000000000000000000000000000000000000000000000000
χ1014-4-4-44-444-244-4-4-4-44422-222-2-2-2-22222-2-2-4400000000222-2-22-2-20000000000000000000000000000000000000000000000000000
χ1024-4-4-44-444-2-4-444-4-44422-222-2-222-2-2-2-2224-40000000022-222-2-2-20000000000000000000000000000000000000000000000000000

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