Finite Group Databasebeta

← Group #13170525

Character table — Group #13170525

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11222222222224444444444444444444466668888888888888812121212121212121212121212121212121212121818242424242424242424242424242424243636363636363636363636363636363636108108
order1223334466666333666666666121212121212121222443666612121212121212121222226666666666661212121288666666666666661212224466668121212122424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-11111-1-111-1-1111111-1-1-1-1111-11-111-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-11-11-1-111-1-1-111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1111111
χ5111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-111111111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1
χ6111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-11-11-1-111-1-1-111-1-1-1-111
χ7111111111111111111111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-11-11-111-1-1-111-1-1-1-1-1-111
χ8111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1
χ911-1111-11-1-1111111-1-1-1-1-1-1111-111-1-11111-11-11-1-1-1111-1-1-111-1-11-11-111-1-111-1-111-1-111-1-1111-11-11-111-1-111-1-11-111-1-11111-1-1-1-1-111-1-11-1
χ1011-1111-11-1-1111111-1-1-1-1-1-1111-111-1-11111-11-11-1-1-1111-1-1-111-1-11-1-1111-1-111-1-1-1-11111-1-1-1-11-1-111-111-1-1-1-1111-11-1-1111-1-11-1-111-1-111-11
χ1111-1111-11-1-1111111-1-1-1-1-1-1111-111-1-11111-11-11-1-1-1111-1-1-111-1-1-111-111-1-1-1-11111-1-111-1-1-1-1-111-11-1-1-11111-1-11-1-111-1-1-111111-1-1-1-111-11
χ1211-1111-11-1-1111111-1-1-1-1-1-1111-111-1-11111-11-11-1-1-1111-1-1-111-1-1-11-1111-1-1-1-111-1-11111-1-111-11-111-1-1-111-1-1111-1-1-111-1-1-1-1-1111111-1-11-1
χ1311-1111-11-1-1111111-1-1-1-1-1-1111-111-1-1111-11-111-1-1-1111-1-1-111-1-11-11-1-1-11111-1-111-1-1-1-111111-11-1-1111-1-111-1-1-11-1-111-1-1-1-1-1111111-1-1-11
χ1411-1111-11-1-1111111-1-1-1-1-1-1111-111-1-1111-11-111-1-1-1111-1-1-111-1-11-1-11-1-11111-1-1-1-111-1-111-1-11-1-11-1111-1-1-1-111-11-111-1-1-111111-1-1-1-1111-1
χ1511-1111-11-1-1111111-1-1-1-1-1-1111-111-1-1111-11-111-1-1-1111-1-1-111-1-1-111-1-1-111-1-11111-1-1-1-111-1-1-111-1-11-1-11111-1-1-111-1-1111-1-11-1-111-1-1111-1
χ1611-1111-11-1-1111111-1-1-1-1-1-1111-111-1-1111-11-111-1-1-1111-1-1-111-1-1-11-11-1-111-1-111-1-111-1-11111-11-11-11-1-111-1-111-1111-1-11111-1-1-1-1-111-1-1-11
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χ18222222-2-222222222222222222-2-2-2-2-2-2-2-2-222-222222-2-2-2-2-2-2-2-2-20000-2-2220000000022-2-2000000-22000000002-20000000000000000000
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χ2322222-1-2-22222-1-12-12-122-1-12-1-1-2-21-2111-22-2-22-1-1-1-1-1-21-211111100002-1-210000−i3i3−i3i3-212-1000000-110000−i3i3−i3i31-1000000−i3i3000−i3i3000000
χ2422222-1-2-22222-1-12-12-122-1-12-1-1-2-21-2111-22-2-22-1-1-1-1-1-21-211111100002-1-210000i3−i3i3−i3-212-1000000-110000i3−i3i3−i31-1000000i3−i3000i3−i3000000
χ2522222-1-2-22222-1-12-12-122-1-12-1-1-2-21-2111-2-222-2-1-1-1-1-1-21-21111110000-212-10000−i3i3−i3i32-1-210000001-10000−i3i3−i3i3-11000000i3−i3000i3−i3000000
χ2622222-1-2-22222-1-12-12-122-1-12-1-1-2-21-2111-2-222-2-1-1-1-1-1-21-21111110000-212-10000i3−i3i3−i32-1-210000001-10000i3−i3i3−i3-11000000−i3i3000−i3i3000000
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χ282222-1222222-12-1-12-12-1-122-12-12-12-12-1-122222-1-1-1-1-1-12-12-1-1-1-1-1-2-200-12-1211110000-12-1200-2-200-1-111110000-1-1-20-20110001100000000
χ292222-1222222-12-1-12-12-1-122-12-12-12-12-1-12-2-2-2-2-1-1-1-1-1-12-12-1-1-1-1-122001-21-2-1-1-1-100001-21-200220011-1-1-1-1000011-20-20110001100000000
χ302222-1222222-12-1-12-12-1-122-12-12-12-12-1-12-2-2-2-2-1-1-1-1-1-12-12-1-1-1-1-1-2-2001-21-2111100001-21-200-2-2001111110000112020-1-1000-1-100000000
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χ342222-12-2-2222-12-1-12-12-1-122-12-1-21-21-211-2-222-2-1-1-1-1-11-21-21111100001-2-12i3−i3i3−i30000-121-20000001-1i3−i3i3−i30000-110000−i3i3000−i3i300000000
χ35222-12222-1-1-1222-1-122-1-1-1-1-1-12-1222222-10000-12-1-1-1-1-1-1-12-1-1-1-12222000022222222000022-1-1-1-100-1-1-1-1-1-1-1-1000000000020000-1-1-1-100
χ36222-12222-1-1-1222-1-122-1-1-1-1-1-12-1222222-10000-12-1-1-1-1-1-1-12-1-1-1-122-2-200002222-2-2-2-20000-2-2-1-11100-1-1-1-111110000000000-20000111100
χ37222-12222-1-1-1222-1-122-1-1-1-1-1-12-1222222-10000-12-1-1-1-1-1-1-12-1-1-1-1-2-2220000-2-2-2-222220000-2-211-1-1001111-1-1-1-10000000000-20000111100
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χ3922-22222-2-2-2222222-2-2-2-2-2-22222-2-222-2-2-222-2-22-2-2-22-2-2222-2-2220000222200000000-2-2-2-20000002200000000-2-20000000000000000000
χ4022-22222-2-2-2222222-2-2-2-2-2-22222-2-222-2-2-2-2-2222-2-2-22-2-2222-2-2220000-2-2-2-2000000002222000000-2-200000000220000000000000000000
χ4122-222-12-2-2-222-1-12-1-21-2-2112-1-12-212-111-222-2-2-1111-1-212-1-111-1-100002-12-10000−i3i3i3−i3-21-21000000-1-10000−i3i3i3−i311000000−i3i3000i3−i3000000
χ4222-222-12-2-2-222-1-12-1-21-2-2112-1-12-212-111-222-2-2-1111-1-212-1-111-1-100002-12-10000i3−i3−i3i3-21-21000000-1-10000i3−i3−i3i311000000i3−i3000−i3i3000000
χ4322-222-12-2-2-222-1-12-1-21-2-2112-1-12-212-111-2-2-222-1111-1-212-1-111-1-10000-21-210000−i3i3i3−i32-12-1000000110000−i3i3i3−i3-1-1000000i3−i3000−i3i3000000
χ4422-222-12-2-2-222-1-12-1-21-2-2112-1-12-212-111-2-2-222-1111-1-212-1-111-1-10000-21-210000i3−i3−i3i32-12-1000000110000i3−i3−i3i3-1-1000000−i3i3000i3−i3000000
χ4522-222-1-22-2-222-1-12-1-21-2-2112-1-1-22-1-21-1-122-22-2-1111-12-1-211-1-111002-22-1-210000-1-1112-1-2100002-2-110000-1-111-11020-200-1-100011000000
χ4622-222-1-22-2-222-1-12-1-21-2-2112-1-1-22-1-21-1-122-22-2-1111-12-1-211-1-11100-222-1-21000011-1-12-1-210000-22-11000011-1-1-110-2020011000-1-1000000
χ4722-222-1-22-2-222-1-12-1-21-2-2112-1-1-22-1-21-1-12-22-22-1111-12-1-211-1-111002-2-212-10000-1-111-212-100002-21-10000-1-1111-10-2020011000-1-1000000
χ4822-222-1-22-2-222-1-12-1-21-2-2112-1-1-22-1-21-1-12-22-22-1111-12-1-211-1-11100-22-212-1000011-1-1-212-10000-221-1000011-1-11-1020-200-1-100011000000
χ4922-22-122-2-2-22-12-1-121-211-2-2-12-121-2-1211-222-2-2-1111-11-2-12-111-1-10000-12-12−i3i3i3−i300001-21-2000000-1-1−i3i3i3−i30000110000−i3i3000i3−i300000000
χ5022-22-122-2-2-22-12-1-121-211-2-2-12-121-2-1211-222-2-2-1111-11-2-12-111-1-10000-12-12i3−i3−i3i300001-21-2000000-1-1i3−i3−i3i30000110000i3−i3000−i3i300000000
χ5122-22-122-2-2-22-12-1-121-211-2-2-12-121-2-1211-2-2-222-1111-11-2-12-111-1-100001-21-2−i3i3i3−i30000-12-1200000011−i3i3i3−i30000-1-10000i3−i3000−i3i300000000
χ5222-22-122-2-2-22-12-1-121-211-2-2-12-121-2-1211-2-2-222-1111-11-2-12-111-1-100001-21-2i3−i3−i3i30000-12-1200000011i3−i3−i3i30000-1-10000−i3i3000i3−i300000000
χ5322-22-12-22-2-22-12-1-121-211-2-2-12-1-2-121-2-1-122-22-2-1111-1-121-21-1-1112-200-121-2-1-1110000-121-2002-200-11-1-1110000-1120-20-1-10001100000000
χ5422-22-12-22-2-22-12-1-121-211-2-2-12-1-2-121-2-1-122-22-2-1111-1-121-21-1-111-2200-121-211-1-10000-121-200-2200-1111-1-10000-11-202011000-1-100000000
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χ5622-22-12-22-2-22-12-1-121-211-2-2-12-1-2-121-2-1-12-22-22-1111-1-121-21-1-111-22001-2-1211-1-100001-2-1200-22001-111-1-100001-120-20-1-10001100000000
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χ5822-2-122-2211-1222-1-1-2-21111-1-12122-2-222-10000-1-211-1-1-111-2-1-1112-2-22000022-2-2-2-2220000-2-2-111-100-1-11111-1-100000000002000011-1-100
χ5922-2-122-2211-1222-1-1-2-21111-1-12122-2-222-10000-1-211-1-1-111-2-1-111-222-20000-2-22222-2-20000-2-21-1-110011-1-1-1-11100000000002000011-1-100
χ6022-2-122-2211-1222-1-1-2-21111-1-12122-2-222-10000-1-211-1-1-111-2-1-111-22-220000-2-222-2-2220000221-11-10011-1-111-1-10000000000-20000-1-11100
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χ8044-4-24-24-422-24-2-2-21-4222-1-1-21-2-2-424-2222000012-1-112-1-21-2-1-1110000000000002i3−2i3−2i32i30000000000000000−i3i3i3−i3000000000000000000000
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χ8344-4-2-244-422-2-24-21-22-4-1-1221-2-2-22-4-24222000012-1-11-121-2-2-1-11100000000−2i32i32i3−2i30000000000000000i3−i3−i3i30000000000000000000000000
χ8444-4-2-244-422-2-24-21-22-4-1-1221-2-2-22-4-24222000012-1-11-121-2-2-1-111000000002i3−2i3−2i32i30000000000000000−i3i3i3−i30000000000000000000000000
χ8544-4-2-24-4422-2-24-21-22-4-1-1221-2-22-242-4-2-2-2000012-1-111-2-12211-1-14-4000000-2-2220000000000-22000011-1-10000000000000000000000000
χ8644-4-2-24-4422-2-24-21-22-4-1-1221-2-22-242-4-2-2-2000012-1-111-2-12211-1-1-4400000022-2-200000000002-20000-1-1110000000000000000000000000
χ874-404440000-4-4-4444000000-4-4-40000000000004000-40000000000000000000000000000022−220000000000000000000000000000022−220000
χ884-404440000-4-4-4444000000-4-4-40000000000004000-400000000000000000000000000000−222200000000000000000000000000000−22220000
χ894-40-24400−2i32i32-4-44-2-200−2i32i3−2i32i322-4000000000000-20−2i32i320000000000000000000000000000022−2200000000000000000000000000000−22i6−i600
χ904-40-24400−2i32i32-4-44-2-200−2i32i3−2i32i322-4000000000000-20−2i32i3200000000000000000000000000000−2222000000000000000000000000000002−2−i6i600
χ914-40-244002i3−2i32-4-44-2-2002i3−2i32i3−2i322-4000000000000-202i3−2i320000000000000000000000000000022−2200000000000000000000000000000−22−i6i600
χ924-40-244002i3−2i32-4-44-2-2002i3−2i32i3−2i322-4000000000000-202i3−2i3200000000000000000000000000000−2222000000000000000000000000000002−2i6−i600
χ93888-4-4-488-4-4-4-4-4222-4-42222222-4-4-4-4-422-40000-12-1-1-122222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ94888-4-4-4-8-8-4-4-4-4-4222-4-4222222244444-2-240000-12-1-1-1-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ9588-8-4-4-48-844-4-4-422244-2-2-2-2222-444-4-4-2-240000-1-211-1-2-222211-1-1000000000000000000000000000000000000000000000000000000000
χ9688-8-4-4-4-8844-4-4-422244-2-2-2-22224-4-44422-40000-1-211-122-2-2-2-1-111000000000000000000000000000000000000000000000000000000000
χ978-8088-40000-8-84-48-4000000-844000000000000-40004000000000000000000000000000000000000000000000000000000000000000000
χ988-808-480000-84-8-4-480000004-84000000000000-40004000000000000000000000000000000000000000000000000000000000000000000
χ998-808-4-40000-8442-4-400000044-2000006i−6i000002000-2000006i−6i00000000000000000000000000000000000000000000000000000000000
χ1008-808-4-40000-8442-4-400000044-200000−6i6i000002000-200000−6i6i00000000000000000000000000000000000000000000000000000000000
χ1018-80-48-400−4i34i34-84-4-4200−4i34i32i3−2i34-24000000000000202i3−2i3-2000000000000000000000000000000000000000000000000000000000000000000
χ1028-80-48-4004i3−4i34-84-4-42004i3−4i3−2i32i34-2400000000000020−2i32i3-2000000000000000000000000000000000000000000000000000000000000000000
χ1038-80-4-4800−4i34i344-8-42-4002i3−2i3−4i34i3-244000000000000202i3−2i3-2000000000000000000000000000000000000000000000000000000000000000000
χ1048-80-4-48004i3−4i344-8-42-400−2i32i34i3−4i3-24400000000000020−2i32i3-2000000000000000000000000000000000000000000000000000000000000000000
χ1058-80-4-4-400−4i34i3444222002i3−2i32i3−2i3-2-2-2000006i−6i00000-10−i3i3100000−3i3i33−33000000000000000000000000000000000000000000000000000000000
χ1068-80-4-4-400−4i34i3444222002i3−2i32i3−2i3-2-2-200000−6i6i00000-10−i3i31000003i−3i−3333000000000000000000000000000000000000000000000000000000000
χ1078-80-4-4-4004i3−4i344422200−2i32i3−2i32i3-2-2-2000006i−6i00000-10i3−i3100000−3i3i−3333000000000000000000000000000000000000000000000000000000000
χ1088-80-4-4-4004i3−4i344422200−2i32i3−2i32i3-2-2-200000−6i6i00000-10i3−i31000003i−3i33−33000000000000000000000000000000000000000000000000000000000

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