Finite Group Databasebeta

← Group #13155710

Character table — Group #13155710

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222222244444444444444444444448888888888881212121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636365454545472727272
order1222333446666666663336666666661212121212121212121236661212121212121212444488242424242424242424242424242424241212121212121212121212121212121244448824242424444412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-11111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111111111111111111111111-1-111111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111
χ91-1-11111-11-1-11-1-1-1-111111-1-1-1-1111-1-1-11111-1-1-1-111-1-1111-1-111-1-1i−ii−ii−iiiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−iii−i−iii−i−i1-11-11-111-1-1ii−i−i1-11-1
χ101-1-11111-11-1-11-1-1-1-111111-1-1-1-1111-1-1-11111-1-1-1-111-1-1111-1-111-1-1i−ii−i−ii−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−iii−i−iii−i−i-11-111-111-1-1−i−iii-11-11
χ111-1-11111-11-1-11-1-1-1-111111-1-1-1-1111-1-1-11111-1-1-1-111-1-1111-1-111-1-1i−i−iii−iiiiiiiii−i−i−i−i−i−i−i−iii−i−i−i−iiiii−i−i−i−iii1-1-11-11-1-111−i−iii1-1-11
χ121-1-11111-11-1-11-1-1-1-111111-1-1-1-1111-1-1-11111-1-1-1-111-1-1111-1-111-1-1i−i−ii−ii−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−iiiii−i−i−i−iii-111-1-11-1-111ii−i−i-111-1
χ131-1-11111-11-1-11-1-1-1-111111-1-1-1-1111-1-1-11111-1-1-1-111-1-1111-1-111-1-1−iii−ii−iiiiiiiii−i−i−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii−i−i-111-1-11-1-111−i−iii-111-1
χ141-1-11111-11-1-11-1-1-1-111111-1-1-1-1111-1-1-11111-1-1-1-111-1-1111-1-111-1-1−iii−i−ii−i−i−i−i−i−i−i−iiiiiiiii−i−iiiii−i−i−i−iiiii−i−i1-1-11-11-1-111ii−i−i1-1-11
χ151-1-11111-11-1-11-1-1-1-111111-1-1-1-1111-1-1-11111-1-1-1-111-1-1111-1-111-1-1−ii−iii−iiiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iii−i−iii−i−iii-11-111-111-1-1ii−i−i-11-11
χ161-1-11111-11-1-11-1-1-1-111111-1-1-1-1111-1-1-11111-1-1-1-111-1-1111-1-111-1-1−ii−ii−ii−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iii−i−iii−i−iii1-11-11-111-1-1−i−iii1-11-1
χ172222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000002-22-20000
χ182222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000-22-220000
χ19222222-12222-122-1-1222-1-122-1-12-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-122220000000000000000002-12-12-12-1-1-1-1-1-1-1-1-1000022-1-1-1-100000000
χ20222222-12222-122-1-1222-1-122-1-12-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-122-2-20000000000000000002-12-1-21-21-1-1-1-111110000-2-2111100000000
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χ22222222-12222-122-1-1222-1-122-1-12-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000000000000000-21-21-21-2111111111000022-1-1-1-100000000
χ2322222-12222-122-1222-1-12-1-1-12-1-12-12-122-1-1-12-1-1-12-1-1-1-12-12-1-1-1-1-100222222-1-1-1-1-1-122-1-1-1-1-1-10000-12-120000-1-1-1-10022000000000000-1-1
χ2422222-12222-122-1222-1-12-1-1-12-1-12-12-122-1-1-12-1-1-12-1-1-1-12-12-1-1-1-1-10022-2-2-2-2111111-2-21111110000-12-120000-1-1-1-100-2-200000000000011
χ2522222-12222-122-1222-1-12-1-1-12-1-12-12-122-1-1-12-1-1-12-1-1-1-12-12-1-1-1-1-100-2-22222-1-1-1-1-1-122-1-1-1-1-1-100001-21-20000111100-2-200000000000011
χ2622222-12222-122-1222-1-12-1-1-12-1-12-12-122-1-1-12-1-1-12-1-1-1-12-12-1-1-1-1-100-2-2-2-2-2-2111111-2-211111100001-21-2000011110022000000000000-1-1
χ272222-12222-122-1222-12-1-12-1-1-12-1-12-122-12-1-1-12-1-12-1-1-1-1-12-12-1-1-1-1220022-1-122-1-1-1-1-1-122-1-1-1-1-12-120000-1-1-1-1000022000000000000-1-100
χ282222-12222-122-1222-12-1-12-1-1-12-1-12-122-12-1-1-12-1-12-1-1-1-1-12-12-1-1-1-12200-2-211-2-2111111-2-21111-12-120000-1-1-1-10000-2-20000000000001100
χ292222-12222-122-1222-12-1-12-1-1-12-1-12-122-12-1-1-12-1-12-1-1-1-1-12-12-1-1-1-1-2-20022-1-122-1-1-1-1-1-122-1-1-1-11-21-2000011110000-2-20000000000001100
χ302222-12222-122-1222-12-1-12-1-1-12-1-12-122-12-1-1-12-1-12-1-1-1-1-12-12-1-1-1-1-2-200-2-211-2-2111111-2-211111-21-200001111000022000000000000-1-100
χ312-2-222222-2-2-22-2-2-2-222222-2-2-2-2222-2-22-2-2-2-22222-22-2-22-2-222-2-2220000000000000000000000000000000000000000000000002i−2i−2i2i0000
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χ332-2-2222-1-22-2-2-1-2-211222-1-1-2-2112-1-11112222-2-2-2-2-1-111-1-1-111-1-1112i−2i2i−2i0000000000000000002i−i−2ii2i−i−2ii−i−iii−i−iii00002-2-1-11100000000
χ342-2-2222-1-22-2-2-1-2-211222-1-1-2-2112-1-11112222-2-2-2-2-1-111-1-1-111-1-1112i−2i−2i2i0000000000000000002i−i−2ii−2ii2i−i−i−iiiii−i−i0000-2211-1-100000000
χ352-2-2222-1-22-2-2-1-2-211222-1-1-2-2112-1-11112222-2-2-2-2-1-111-1-1-111-1-111−2i2i2i−2i000000000000000000−2ii2i−i2i−i−2iiii−i−i−i−iii0000-2211-1-100000000
χ362-2-2222-1-22-2-2-1-2-211222-1-1-2-2112-1-11112222-2-2-2-2-1-111-1-1-111-1-111−2i2i−2i2i000000000000000000−2ii2i−i−2ii2i−iii−i−iii−i−i00002-2-1-11100000000
χ372-2-222-12-22-212-21-2-22-1-12-111-21-12-1-21-22-1-1-1-21112-111-12-1-21-1-111002i−2i2i−2i2i2i−i−i−i−i−i−i−2i−2iiiiiii0000−i2ii−2i0000−i−iii002-2000000000000-11
χ382-2-222-12-22-212-21-2-22-1-12-111-21-12-1-21-22-1-1-1-21112-111-12-1-21-1-111002i−2i−2i2i−2i−2iiiiiii2i2i−i−i−i−i−i−i0000−i2ii−2i0000−i−iii00-220000000000001-1
χ392-2-222-12-22-212-21-2-22-1-12-111-21-12-1-21-22-1-1-1-21112-111-12-1-21-1-11100−2i2i2i−2i2i2i−i−i−i−i−i−i−2i−2iiiiiii0000i−2i−i2i0000ii−i−i00-220000000000001-1
χ402-2-222-12-22-212-21-2-22-1-12-111-21-12-1-21-22-1-1-1-21112-111-12-1-21-1-11100−2i2i−2i2i−2i−2iiiiiii2i2i−i−i−i−i−i−i0000i−2i−i2i0000ii−i−i002-2000000000000-11
χ412-2-22-122-221-221-2-2-2-12-1-12111-2-1-121-2-2-12-1-11-2112-111-1-121-2-1-1112i−2i002i−2i−i−i2i2i−i−i−i−iii−2i−2iiiii−i2ii−2i0000−i−iii00002-2000000000000-1100
χ422-2-22-122-221-221-2-2-2-12-1-12111-2-1-121-2-2-12-1-11-2112-111-1-121-2-1-1112i−2i00−2i2iii−2i−2iiiii−i−i2i2i−i−i−i−i−i2ii−2i0000−i−iii0000-220000000000001-100
χ432-2-22-122-221-221-2-2-2-12-1-12111-2-1-121-2-2-12-1-11-2112-111-1-121-2-1-111−2i2i002i−2i−i−i2i2i−i−i−i−iii−2i−2iiiiii−2i−i2i0000ii−i−i0000-220000000000001-100
χ442-2-22-122-221-221-2-2-2-12-1-12111-2-1-121-2-2-12-1-11-2112-111-1-121-2-1-111−2i2i00−2i2iii−2i−2iiiii−i−i2i2i−i−i−i−ii−2i−i2i0000ii−i−i00002-2000000000000-1100
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χ874-4-444-2-2-44-42-2-42224-2-2-21222-1-2-212-124-2-2-2-4222-21-1-11-212-111-1-100−4i4i00000000000000000000002i2i−2i−2i0000−i−iii000000000000000000
χ884-4-44-2444-42-442-4-4-4-24-2-24222-4-2-242-442-422-24-2-2-4-222-22-4-2422-2-200000000000000000000000000000000000000000000000000000000
χ894-4-44-24-24-42-4-22-422-24-21-222-12-21-2-12-22-422-24-2-221-1-11-121-2-1-1110000000000000000000000000000003i−3i−3i3i0000000000000000000000
χ904-4-44-24-24-42-4-22-422-24-21-222-12-21-2-12-22-422-24-2-221-1-11-121-2-1-111000000000000000000000000000000−3i3i3i−3i0000000000000000000000
χ914-4-44-24-2-442-4-22-422-24-21-222-12-21-2-122-24-2-22-422-21-1-111-2-1211-1-14i−4i00000000000000000000−2i−2i2i2i0000ii−i−i0000000000000000000000
χ924-4-44-24-2-442-4-22-422-24-21-222-12-21-2-122-24-2-22-422-21-1-111-2-1211-1-1−4i4i000000000000000000002i2i−2i−2i0000−i−iii0000000000000000000000
χ934-4-44-2-244-422422-4-4-2-21-2-2-1-1221-2-222422-1-1-2-211-41-1-1122-2-2-1-111000000000033-3-30000-3-3330000000000000000000000000000000000
χ944-4-44-2-244-422422-4-4-2-21-2-2-1-1221-2-222422-1-1-2-211-41-1-1122-2-2-1-1110000000000-3-333000033-3-30000000000000000000000000000000000
χ954-4-44-2-24-4422422-4-4-2-21-2-2-1-1221-2-222-4-2-21122-1-141-1-11-2-22211-1-100004i−4i−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i0000000000000000000000000000000000
χ964-4-44-2-24-4422422-4-4-2-21-2-2-1-1221-2-222-4-2-21122-1-141-1-11-2-22211-1-10000−4i4i2i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii0000000000000000000000000000000000
χ978888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-422-4-422-4-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ988888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444-2-244-2-24-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ9988-8-88-4-400844-8-4-44-84-4-42-44-4-244-242000000000022-2-20000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-48-400-4-8448-444-8-42-4-44244-24-2-4000000000022-2-20000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-400-4444-4-44442222-22-2-2-2-2-220006i−6i006i−6i0-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-400-4444-4-44442222-22-2-2-2-2-22000−6i6i00−6i6i0-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-400-8-44844-4-84-4-424-44244-2-4-200000000002-22-20000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-48-400484-4-84-44-8-42-44-4-2-44-242400000000002-22-20000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-4004-44-444-444222-22-22-2-2-22-20006i−6i00−6i6i0-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-4004-44-444-444222-22-22-2-2-22-2000−6i6i006i−6i0-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-48-844-44444-4-4222-2-2-2-2222-2-2-444-2-2-4-4224-111-1-2-22211-1-100000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4-8844-44444-4-4222-2-2-2-2222-2-24-4-42244-2-2-4-111-122-2-2-1-11100000000000000000000000000000000000000000000000000000000

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