Finite Group Databasebeta

← Group #10824483

Character table — Group #10824483

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order12222222344444444444466666661212121212121212888888881212121212121212242424242424242424242424242424242244444466661212121212121212121212122222444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1111111-1-111-1-1-1-1
χ911111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-111111-11-1-1-1-1-111-1-1
χ1011111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-111
χ1111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111111-11-11-1-1-1-1-1-111
χ1211111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11-11-1111111-1-1
χ1311111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-11-11-1-1-111-1-111
χ1411111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-11-1111-1-111-1-1
χ1511111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-1-11-11-1-11111-1-1
χ1611111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1111-11-111-1-1-1-111
χ17222222222-2-22222-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000002-2-2200000000
χ18222222222-2-22222-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000-222-200000000
χ19222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-2-2-200000000-2-22222-2-20000000000000000000000000000000000000000000022-2-200000000
χ20222222222-2-2-2-2-2-22222-2-22222222-2-2-2-2-2-2-2-200000000-2-22222-2-200000000000000000000000000000000000000000000-2-22200000000
χ2122222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ2322222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-111111111-1-1-1-10000000000000000
χ2422222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-222221111-1-1-1-1-1-1-1-111110000000000000000
χ2522222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1111111112222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2622222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1111111112222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-111111111-2-222-2-22211111111-1-1-1-1-1-1-1-10000000000000000
χ2722222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-11111-1-1-1-111110000000000000000
χ2822222222-122-2-2-2-2-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-11111-1-1-1-10000000000000000
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χ44222-2-22-2-2-1-22−2i−2i2i2i2i2i−2i−2i-22-11-11-111iiii−i−i−i−i000000001-1−i−iii1-1−3−3−3−33333−i3−i3−i3−i3i3i3i3i3-222i−2i000011-1-133−3−3i3i3−i3−i3−i−iii0000000000000000
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χ4622-22-2-22-222-22i−2i2i−2i2i−2i2i−2i-22-222-2-22-22i2i−2i−2i2i2i−2i−2i000000002-22i−2i2i−2i-220000000000000000000000000000000000000000000000000000-22−2i2i
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χ4822-22-2-22-222-2−2i2i−2i2i−2i2i−2i2i-22-222-2-22-2−2i−2i2i2i−2i−2i2i2i000000002-2−2i2i−2i2i-220000000000000000000000000000000000000000000000000000-222i−2i
χ4922-22-2-22-22-222i−2i2i−2i−2i2i−2i2i2-2-222-2-22-22i2i−2i−2i2i2i−2i−2i22-2-22i2i−2i−2i-22−2i2i−2i2i2-222-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ5022-22-2-22-22-222i−2i2i−2i−2i2i−2i2i2-2-222-2-22-22i2i−2i−2i2i2i−2i−2i-2-222−2i−2i2i2i-22−2i2i−2i2i2-2-2-222-2-222−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ5122-22-2-22-22-22−2i2i−2i2i2i−2i2i−2i2-2-222-2-22-2−2i−2i2i2i−2i−2i2i2i22-2-2−2i−2i2i2i-222i−2i2i−2i2-222-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ5222-22-2-22-22-22−2i2i−2i2i2i−2i2i−2i2-2-222-2-22-2−2i−2i2i2i−2i−2i2i2i-2-2222i2i−2i−2i-222i−2i2i−2i2-2-2-222-2-2222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ5322-22-2-22-2-1-222i−2i2i−2i−2i2i−2i2i2-21-1-111-11−i−iii−i−iii22-2-22i2i−2i−2i1-1i−ii−i-11-1-111-1-111−i−iii−i−iii00000000−i3i3−i3i3−i3i3−i3i33−33−33−33−30000000000000000
χ5422-22-2-22-2-1-222i−2i2i−2i−2i2i−2i2i2-21-1-111-11−i−iii−i−iii22-2-22i2i−2i−2i1-1i−ii−i-11-1-111-1-111−i−iii−i−iii00000000i3−i3i3−i3i3−i3i3−i3−33−33−33−330000000000000000
χ5522-22-2-22-2-1-222i−2i2i−2i−2i2i−2i2i2-21-1-111-11−i−iii−i−iii-2-222−2i−2i2i2i1-1i−ii−i-1111-1-111-1-1ii−i−iii−i−i00000000−i3i3−i3i3i3−i3i3−i3−33−333−33−30000000000000000
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χ6122-2-22-2-222222-2-222-2-22-2-2-2-222-2-2222-2-2-2-22200000000222-2-22-2-2000000000000000000002i−2i2i−2i00002i−2i−2i2i−2i2i2i−2i00000000000000000000
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χ6522-2-22-2-222-2-22-2-22-222-222-2-222-2-2222-2-2-2-22200000000-2-2-222-2220000000000000000000000000000000000000000002-20000002-20000
χ6622-2-22-2-222-2-22-2-22-222-222-2-222-2-2222-2-2-2-22200000000-2-2-222-222000000000000000000000000000000000000000000-22000000-220000
χ6722-2-22-2-222-2-2-222-22-2-2222-2-222-2-22-2-22222-2-200000000-2-22-2-22220000000000000000000000000000000000000000002-2000000-220000
χ6822-2-22-2-222-2-2-222-22-2-2222-2-222-2-22-2-22222-2-200000000-2-22-2-2222000000000000000000000000000000000000000000-220000002-20000
χ6922-2-22-2-22-1222-2-222-2-22-2-211-1-111-1-1-11111-1-100000000-1-1-111-11133−3−3−3−333−3−33333−3−300002i−2i2i−2i−i3i3i3−i3−iii−ii−i−ii−i3i3i3−i30000000000000000
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χ7622-2-22-2-22-122-222-2-222-2-2-211-1-111-111-1-1-1-11100000000-1-11-1-1111−3−33333−3−3−3−33333−3−30000−2i2i2i−2i−i3i3i3−i3i−i−iii−i−iii3−i3−i3i30000000000000000
χ7744444444-2-4-44444-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222222200000000000000000000000000000000000000000000000000000000
χ7844444444-2-4-4-4-4-4-44444-4-4-2-2-2-2-2-2-2222222220000000022-2-2-2-22200000000000000000000000000000000000000000000000000000000
χ79444-4-44-4-4-24-44i4i−4i−4i4i4i−4i−4i4-4-22-22-222−2i−2i−2i−2i2i2i2i2i00000000-22−2i−2i2i2i-2200000000000000000000000000000000000000000000000000000000
χ80444-4-44-4-4-24-4−4i−4i4i4i−4i−4i4i4i4-4-22-22-2222i2i2i2i−2i−2i−2i−2i00000000-222i2i−2i−2i-2200000000000000000000000000000000000000000000000000000000
χ8144-44-4-44-4-24-44i−4i4i−4i4i−4i4i−4i-442-2-222-22−2i−2i2i2i−2i−2i2i2i00000000-22−2i2i−2i2i2-200000000000000000000000000000000000000000000000000000000
χ8244-44-4-44-4-24-4−4i4i−4i4i−4i4i−4i4i-442-2-222-222i2i−2i−2i2i2i−2i−2i00000000-222i−2i2i−2i2-200000000000000000000000000000000000000000000000000000000
χ8344-4-44-4-44-2-4-44-4-44-444-44422-2-222-2-2-22222-2-200000000222-2-22-2-200000000000000000000000000000000000000000000000000000000
χ8444-4-44-4-44-2-4-4-444-44-4-444422-2-222-222-2-2-2-2220000000022-222-2-2-200000000000000000000000000000000000000000000000000000000
χ854-4444-4-4-4400000000000044-4-4-4-44000000000000−2i22i2−2i22i20000000000000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000000000000000000000
χ864-4444-4-4-4400000000000044-4-4-4-440000000000002i2−2i22i2−2i200000000000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000000000000000000000
χ874-4444-4-4-4-2000000000000-2-22222-2−2i32i3−2i32i3−2i32i3−2i32i30000−2i22i2−2i22i2000000006−66−66−66−6i2−i2i2−i2i2−i2i2−i20000000000000000000000000000000000000000
χ884-4444-4-4-4-2000000000000-2-22222-2−2i32i3−2i32i3−2i32i3−2i32i300002i2−2i22i2−2i200000000−66−66−66−66−i2i2−i2i2−i2i2−i2i20000000000000000000000000000000000000000
χ894-4444-4-4-4-2000000000000-2-22222-22i3−2i32i3−2i32i3−2i32i3−2i30000−2i22i2−2i22i200000000−66−66−66−66i2−i2i2−i2i2−i2i2−i20000000000000000000000000000000000000000
χ904-4444-4-4-4-2000000000000-2-22222-22i3−2i32i3−2i32i3−2i32i3−2i300002i2−2i22i2−2i2000000006−66−66−66−6−i2i2−i2i2−i2i2−i2i20000000000000000000000000000000000000000
χ914-44-4-4-44440000000000004-4-44-44-40000000022−2222−2200000000000022−2222−22−2222−2222000000000000000000000000000000000000000000000000
χ924-44-4-4-44440000000000004-4-44-44-400000000−2222−2222000000000000−2222−222222−2222−22000000000000000000000000000000000000000000000000
χ934-44-4-4-444-2000000000000-222-22-2223−2323−23−2323−232322−2222−22000000000000−22−222−22−26−66−6−66−660000000000000000000000000000000000000000
χ944-44-4-4-444-2000000000000-222-22-2223−2323−23−2323−2323−2222−22220000000000002−22−2−22−22−66−666−66−60000000000000000000000000000000000000000
χ954-44-4-4-444-2000000000000-222-22-22−2323−232323−2323−2322−2222−22000000000000−22−222−22−2−66−666−66−60000000000000000000000000000000000000000
χ964-44-4-4-444-2000000000000-222-22-22−2323−232323−2323−23−2222−22220000000000002−22−2−22−226−66−6−66−660000000000000000000000000000000000000000
χ974-4-44-44-444000000000000-44-444-4-400000000000022−22−2222000000000000000022−22−222222−22−22220000000000000000000000000000000000000000
χ984-4-44-44-444000000000000-44-444-4-4000000000000−222222−220000000000000000−222222−22−222222−220000000000000000000000000000000000000000
χ994-4-44-44-44-20000000000002-22-2-22223−23−232323−23−2323000022−22−2222000000006−6−666−6−66−222−2−222−20000000000000000000000000000000000000000
χ1004-4-44-44-44-20000000000002-22-2-22223−23−232323−23−23230000−222222−2200000000−666−6−666−62−2−222−2−220000000000000000000000000000000000000000
χ1014-4-44-44-44-20000000000002-22-2-222−232323−23−232323−23000022−22−222200000000−666−6−666−6−222−2−222−20000000000000000000000000000000000000000
χ1024-4-44-44-44-20000000000002-22-2-222−232323−23−232323−230000−222222−22000000006−6−666−6−662−2−222−2−220000000000000000000000000000000000000000
χ1034-4-4-4444-44000000000000-4-4-4-44440000000022−22−222200000000000022−22−2222−222222−22000000000000000000000000000000000000000000000000
χ1044-4-4-4444-44000000000000-4-4-4-444400000000−222222−22000000000000−222222−2222−22−2222000000000000000000000000000000000000000000000000
χ1054-4-4-4444-4-20000000000002222-2-2-2−2i32i32i3−2i32i3−2i3−2i32i322−22−2222000000000000−222−22−2−22−i6i6i6−i6i6−i6−i6i60000000000000000000000000000000000000000
χ1064-4-4-4444-4-20000000000002222-2-2-2−2i32i32i3−2i32i3−2i3−2i32i3−222222−220000000000002−2−22−222−2i6−i6−i6i6−i6i6i6−i60000000000000000000000000000000000000000
χ1074-4-4-4444-4-20000000000002222-2-2-22i3−2i3−2i32i3−2i32i32i3−2i322−22−2222000000000000−222−22−2−22i6−i6−i6i6−i6i6i6−i60000000000000000000000000000000000000000
χ1084-4-4-4444-4-20000000000002222-2-2-22i3−2i3−2i32i3−2i32i32i3−2i3−222222−220000000000002−2−22−222−2−i6i6i6−i6i6−i6−i6i60000000000000000000000000000000000000000

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