Finite Group Databasebeta

← Group #10858783

Character table — Group #10858783

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222244444444444444444444444444444444444444888888888888888888888812121212242424242424242424244848
order12222222344444444666666612121212121212122244446666888888881212121224242424242424242424242424242424444444121212121212121212121212121212124444224444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ61111111111111111111111111111111111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ71111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1
χ911111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1-1-1111-1
χ1011111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1111-1-1-11
χ1111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-11-111-1-1-11
χ1211111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111-11-1-1111-1
χ1311111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1-1-111-11
χ1411111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1111-1-11-1
χ1511111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111-111-1-11-1
χ1611111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11-1-111-11
χ17222222222-2-22222-2-2222222222222222-2-20000-2-2-2-200000000-2-2-2-20000000000000000000000000000000000000022220000-2-2000000
χ18222222222-2-22222-2-2222222222222222-2-20000-2-2-2-200000000-2-2-2-200000000000000000000000000000000000000-2-2-2-2000022000000
χ19222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2220000222200000000-2-2-2-20000000000000000000000000000000000000022-2-20000-22000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2220000222200000000-2-2-2-200000000000000000000000000000000000000-2-22200002-2000000
χ2122222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-2-222-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2322222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111111111110000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111122-2-22211111111-1-1-1-1-1-1-1-10000000000000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-2222211112222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111122-2-2-2-2-1-1-1-11111-1-1-1-111110000000000000000
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χ2722222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2-2-2-211112222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111-2-222221111-1-1-1-11111-1-1-1-10000000000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2-2-2-21111-2-2-2-22222-1-1-1-111111111-1-1-1-1-1-1-1-12222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ29222-2-22-2-222222-2-2-2-2222-2-2-2-22222-2-2-2-22-2000022-2-20000000022-2-20000000000000000000000000000000000000000002-22-200000000
χ30222-2-22-2-222222-2-2-2-2222-2-2-2-22222-2-2-2-22-2000022-2-20000000022-2-2000000000000000000000000000000000000000000-22-2200000000
χ31222-2-22-2-2222-2-222-2-2222-2-2-2-2-2-2-2-22222-220000-2-2220000000022-2-20000000000000000000000000000000000000000002-2-2200000000
χ32222-2-22-2-2222-2-222-2-2222-2-2-2-2-2-2-2-22222-220000-2-2220000000022-2-2000000000000000000000000000000000000000000-222-200000000
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χ41222-2-22-2-2-1-2-2-2-22222-1-1-111111111-1-1-1-12-22i2i−2i−2i-1-1110000000011-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i300−2i2i00−i−iiiii−i−i33−3−3−3−3330000000000000000
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χ43222-2-22-2-2-1-2-2-2-22222-1-1-111111111-1-1-1-12-2−2i−2i2i2i-1-1110000000011-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3002i−2i00ii−i−i−i−iii−3−33333−3−30000000000000000
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χ5122-22-2-22-2200−2i2i−2i2i002-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000i2i2−i2−i222−2−20000i2i2−i2−i2i2i2−i2−i222−2−222−2−200000000000000000000002i−2i-22000000−i2i2−2200
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χ662-22-22-22-22-2200002-2-2-22-22-2200000000002-2-220000−2i2i−2i2i0000-222-2−2i2i−2i2i2i−2i2i−2i00000000−2i2i00002-2-2200002i−2i−2i2i00000000000000000000
χ672-22-22-22-22-2200002-2-2-22-22-220000000000-222-200002i−2i2i−2i0000-222-22i−2i2i−2i−2i2i−2i2i00000000−2i2i0000-222-200002i−2i−2i2i00000000000000000000
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χ692-22-22-22-2-1-2200002-211-11-11-1−i3i3−i3i3i3−i3i3−i3002-2-22i3−i3−i3i32i−2i2i−2i00001-1-11−ii−iii−ii−i3−33−3−33−332i−2i0000-111-1−i3i3i3−i3i−i−ii−333−30000000000000000
χ702-22-22-22-2-1-2200002-211-11-11-1−i3i3−i3i3i3−i3i3−i3002-2-22i3−i3−i3i3−2i2i−2i2i00001-1-11i−ii−i−ii−ii−33−333−33−3−2i2i0000-111-1−i3i3i3−i3−iii−i3−3−330000000000000000
χ712-22-22-22-2-1-2200002-211-11-11-1−i3i3−i3i3i3−i3i3−i300-222-2i3−i3−i3i32i−2i2i−2i00001-1-11−ii−iii−ii−i3−33−3−33−33−2i2i00001-1-11i3−i3−i3i3−iii−i3−3−330000000000000000
χ722-22-22-22-2-1-2200002-211-11-11-1−i3i3−i3i3i3−i3i3−i300-222-2i3−i3−i3i3−2i2i−2i2i00001-1-11i−ii−i−ii−ii−33−333−33−32i−2i00001-1-11i3−i3−i3i3i−i−ii−333−30000000000000000
χ732-22-22-22-2-1-2200002-211-11-11-1i3−i3i3−i3−i3i3−i3i3002-2-22−i3i3i3−i32i−2i2i−2i00001-1-11−ii−iii−ii−i−33−333−33−32i−2i0000-111-1i3−i3−i3i3i−i−ii3−3−330000000000000000
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χ934-444-4-4-44-2-440000-4422-2-22-222i3−2i32i3−2i32i3−2i32i3−2i3000000−2i32i3−2i32i3000000002-22-2000000000000000000000000000000000000000000000000000000
χ944-44-44-44-444-40000-44-4-44-44-44000000000000000000000000004-4-44000000000000000000000000000000000000000000000000000000
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χ964-44-44-44-4-24-40000-4422-22-22-22i3−2i32i3−2i3−2i32i3−2i32i30000002i3−2i3−2i32i300000000-222-2000000000000000000000000000000000000000000000000000000
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χ994-4-4444-4-4-2000000002-22-222-223−23−232323−23−232300000000000000−2i22i22i2−2i20000i6−i6−i6i6i6−i6−i6i6i2−i2−i2i2i2−i2−i2i200000000000000000000000000000000000000
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χ1014-4-4444-4-4-2000000002-22-222-2−232323−23−232323−2300000000000000−2i22i22i2−2i20000−i6i6i6−i6−i6i6i6−i6i2−i2−i2i2i2−i2−i2i200000000000000000000000000000000000000
χ1024-4-4444-4-4-2000000002-22-222-2−232323−23−232323−23000000000000002i2−2i2−2i22i20000i6−i6−i6i6i6−i6−i6i6−i2i2i2−i2−i2i2i2−i200000000000000000000000000000000000000
χ1034-4-4-4-4444400000000-44-4-444-400000000000000000022−22−22220000000022−22−2222−222222−220000000000000000000000000000000000000000000000
χ1044-4-4-4-4444400000000-44-4-444-4000000000000000000−222222−2200000000−222222−2222−22−22220000000000000000000000000000000000000000000000
χ1054-4-4-4-4444-2000000002-222-2-2223−23−2323−232323−23000000000022−22−222200000000−222−22−2−226−6−66−666−600000000000000000000000000000000000000
χ1064-4-4-4-4444-2000000002-222-2-2223−23−2323−232323−230000000000−222222−22000000002−2−22−222−2−666−66−6−6600000000000000000000000000000000000000
χ1074-4-4-4-4444-2000000002-222-2-22−232323−2323−23−2323000000000022−22−222200000000−222−22−2−22−666−66−6−6600000000000000000000000000000000000000
χ1084-4-4-4-4444-2000000002-222-2-22−232323−2323−23−23230000000000−222222−22000000002−2−22−222−26−6−66−666−600000000000000000000000000000000000000

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