Finite Group Databasebeta

← Group #13170548

Character table — Group #13170548

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11222222222224444444444444444444466668888888888888812121212121212121212121212121212121212121818242424242424242424242424242424243636363636363636363636363636363636108108
order12233344666663336666666661212121212121212224436666121212121212121212224466666666121212121212121288666666661212121212121212224466668121212122424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-111111111-1-111-1-1-1-11-11-1-1-111-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-111111111-1-1-1-111-1-1-1-111111111-11-1111-1-1-1-1-111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111
χ5111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-111111111-1-1111111-1-11111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1
χ6111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-111-1-1-1-111
χ7111111111111111111111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111-11-1-1-111-111-1-1-1-1-1-111
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
χ911-1111-11-1-1111111-1-1-1-1-1-1111-11-11-11111-11-11-1-1-111-1-11-111-1-11-11-11-11-111-1-11-11-111-1-1111-11-111-1-11-11-111-1-11-1-11-1-111-1-1-11111-1-11-1
χ1011-1111-11-1-1111111-1-1-1-1-1-1111-11-11-11111-11-11-1-1-111-1-11-111-1-11-1-111-11-111-1-11-11-1-1-111-1-11-11-111-1-1-111-1-1-11111-1-111111-1-1-1-1-1-111-11
χ1111-1111-11-1-1111111-1-1-1-1-1-1111-11-11-11111-11-11-1-1-111-1-11-111-1-1-111-11-11-1-1-1111-11-111-1-1-1-1-111-1-1-1111-11-111-1-1-1-111-1-1-1-111111-1-111-11
χ1211-1111-11-1-1111111-1-1-1-1-1-1111-11-11-11111-11-11-1-1-111-1-11-111-1-1-11-111-11-1-1-1111-11-1-1-11111-111-1-1-111-111-1-1-111-111-111-1-1-111-1-111-1-11-1
χ1311-1111-11-1-1111111-1-1-1-1-1-1111-11-11-1111-11-111-1-1-111-1-11-111-1-11-11-1-11-1111-1-1-11-1111-1-1111-1-1111-1-11-1-1111-1-1-111-111-1-1-111-1-111-1-1-11
χ1411-1111-11-1-1111111-1-1-1-1-1-1111-11-11-1111-11-111-1-1-111-1-11-111-1-11-1-11-11-1111-1-1-11-11-1-111-1-11-1-1111-1-1-11-11-1-111-1-111-1-1-1-111111-1-1111-1
χ1511-1111-11-1-1111111-1-1-1-1-1-1111-11-11-1111-11-111-1-1-111-1-11-111-1-1-111-1-11-11-1-111-11-1111-1-1-1-1-11-11-1-1111-1-1111-1-111-1-111111-1-1-1-1-1-1111-1
χ1611-1111-11-1-1111111-1-1-1-1-1-1111-11-11-1111-11-111-1-1-111-1-11-111-1-1-11-11-11-11-1-111-11-11-1-11111-11-11-1-111-11-11-1-1111-1-11-1-111-1-1-11111-1-1-11
χ17222222-2-222222222222222222-2-2-2-2-2-2-2-22-2-2222222-2-2-2-2-2-2-2-2-200002-22-20000-22-22000000002-2000000-2200000000000000000000000
χ18222222-2-222222222222222222-2-2-2-2-2-2-2-2-222-222222-2-2-2-2-2-2-2-2-20000-22-2200002-22-200000000-220000002-200000000000000000000000
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χ2422222-1-2-2222-122-1-12-122-1-1-1-12-211-2-211-22-2-22-1-1-1-1-1111-2-2111100002-2-11i3−i3i3−i31-1-2200000000-11i3−i3i3−i3001-10000000000i3−i30i3−i300000000
χ2522222-1-2-2222-122-1-12-122-1-1-1-12-211-2-211-2-222-2-1-1-1-1-1111-2-211110000-221-1−i3i3−i3i3-112-2000000001-1−i3i3−i3i300-110000000000i3−i30i3−i300000000
χ2622222-1-2-2222-122-1-12-122-1-1-1-12-211-2-211-2-222-2-1-1-1-1-1111-2-211110000-221-1i3−i3i3−i3-112-2000000001-1i3−i3i3−i300-110000000000−i3i30−i3i300000000
χ272222-12222222-1-1-12-12-1-1222-1-1222-1-1-1-122222-1-1-1-1-122-1-1-1-1-1-1-10022-1-122000022-1-1-1-1-1-10000-1-1000022-1-1-1-1-1-10202-1-100000-1-1000000
χ282222-12222222-1-1-12-12-1-1222-1-1222-1-1-1-122222-1-1-1-1-122-1-1-1-1-1-1-100-2-2-1-122000022-1-111110000-1-10000-2-2-1-111110-20-2110000011000000
χ292222-12222222-1-1-12-12-1-1222-1-1222-1-1-1-12-2-2-2-2-1-1-1-1-122-1-1-1-1-1-1-1002211-2-20000-2-211-1-1-1-100001100002211-1-1-1-10-20-2110000011000000
χ302222-12222222-1-1-12-12-1-1222-1-1222-1-1-1-12-2-2-2-2-1-1-1-1-122-1-1-1-1-1-1-100-2-211-2-20000-2-21111110000110000-2-21111110202-1-100000-1-1000000
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χ332222-12-2-22222-1-1-12-12-1-1222-1-1-2-2-21111-2-222-2-1-1-1-1-1-2-2111111100001-1-2200002-2-11−i3i3−i3i300001-1000000-11−i3i3−i3i30000i3−i300000i3−i3000000
χ342222-12-2-22222-1-1-12-12-1-1222-1-1-2-2-21111-2-222-2-1-1-1-1-1-2-2111111100001-1-2200002-2-11i3−i3i3−i300001-1000000-11i3−i3i3−i30000−i3i300000−i3i3000000
χ35222-12222-1-1-122-12-122-1-1-1-1-12-1-1222222-10000-12-1-1-1-1-12-1-1-1-1-1-12222000022220000222222-1-100-1-1-1-1-1-100-1-1-1-10000000020000-1-1-1-100
χ36222-12222-1-1-122-12-122-1-1-1-1-12-1-1222222-10000-12-1-1-1-1-12-1-1-1-1-1-122-2-2000022220000-2-2-2-2-2-2-1-100-1-1-1-11100111100000000-20000111100
χ37222-12222-1-1-122-12-122-1-1-1-1-12-1-1222222-10000-12-1-1-1-1-12-1-1-1-1-1-1-2-2220000-2-2-2-200002222-2-211001111-1-100-1-1-1-100000000-20000111100
χ38222-12222-1-1-122-12-122-1-1-1-1-12-1-1222222-10000-12-1-1-1-1-12-1-1-1-1-1-1-2-2-2-20000-2-2-2-20000-2-2-2-22211001111110011110000000020000-1-1-1-100
χ3922-22222-2-2-2222222-2-2-2-2-2-22222-22-22-2-2-222-2-22-2-2-22-222-22-2-222000022220000-2-2-2-20000000022000000-2-200000000000000000000000
χ4022-22222-2-2-2222222-2-2-2-2-2-22222-22-22-2-2-2-2-2222-2-2-22-222-22-2-2220000-2-2-2-20000222200000000-2-20000002200000000000000000000000
χ4122-222-12-2-2-22-122-1-1-21-2-211-1-1221-1-2211-222-2-2-1111-11-1-1-2211-1-1000022-1-1−i3i3i3−i311-2-200000000-1-1−i3i3i3−i300110000000000−i3i30i3−i300000000
χ4222-222-12-2-2-22-122-1-1-21-2-211-1-1221-1-2211-222-2-2-1111-11-1-1-2211-1-1000022-1-1i3−i3−i3i311-2-200000000-1-1i3−i3−i3i300110000000000i3−i30−i3i300000000
χ4322-222-12-2-2-22-122-1-1-21-2-211-1-1221-1-2211-2-2-222-1111-11-1-1-2211-1-10000-2-211−i3i3i3−i3-1-1220000000011−i3i3i3−i300-1-10000000000i3−i30−i3i300000000
χ4422-222-12-2-2-22-122-1-1-21-2-211-1-1221-1-2211-2-2-222-1111-11-1-1-2211-1-10000-2-211i3−i3−i3i3-1-1220000000011i3−i3−i3i300-1-10000000000−i3i30i3−i300000000
χ4522-222-1-22-2-22-122-1-1-21-2-211-1-12-2-112-2-1-122-22-2-1111-1-1112-2-1-1112-2002-2-11-1-111-112-20000002-2-11-1-11100-11000020-2000-1-101100000000
χ4622-222-1-22-2-22-122-1-1-21-2-211-1-12-2-112-2-1-122-22-2-1111-1-1112-2-1-111-22002-2-1111-1-1-112-2000000-22-1111-1-100-110000-202000110-1-100000000
χ4722-222-1-22-2-22-122-1-1-21-2-211-1-12-2-112-2-1-12-22-22-1111-1-1112-2-1-1112-200-221-1-1-1111-1-220000002-21-1-1-111001-10000-202000110-1-100000000
χ4822-222-1-22-2-22-122-1-1-21-2-211-1-12-2-112-2-1-12-22-22-1111-1-1112-2-1-111-2200-221-111-1-11-1-22000000-221-111-1-1001-1000020-2000-1-101100000000
χ4922-22-122-2-2-222-1-1-121-211-2-22-1-12-221-111-222-2-2-1111-1-22-11-111-1-10000-1-1220000-2-211−i3i3i3−i30000-1-100000011−i3i3i3−i30000i3−i300000−i3i3000000
χ5022-22-122-2-2-222-1-1-121-211-2-22-1-12-221-111-222-2-2-1111-1-22-11-111-1-10000-1-1220000-2-211i3−i3−i3i30000-1-100000011i3−i3−i3i30000−i3i300000i3−i3000000
χ5122-22-122-2-2-222-1-1-121-211-2-22-1-12-221-111-2-2-222-1111-1-22-11-111-1-1000011-2-2000022-1-1−i3i3i3−i3000011000000-1-1−i3i3i3−i30000−i3i300000i3−i3000000
χ5222-22-122-2-2-222-1-1-121-211-2-22-1-12-221-111-2-2-222-1111-1-22-11-111-1-1000011-2-2000022-1-1i3−i3−i3i3000011000000-1-1i3−i3−i3i30000i3−i300000−i3i3000000
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χ6022-2-122-2211-122-12-1-2-21111-12-112-22-222-10000-1-211-1-11-2-11-1-111-22-220000-2-2220000-2-222221-10011-1-11-10011-1-100000000-20000-1-11100
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χ8444-4-2-244-422-24-21-2-22-4-1-122-2-21-2-442-2222000012-1-112-2-2-11-1-11100000000000000002i3−2i3−2i32i300000000000000−i3i3i3−i30000000000000000000
χ8544-4-2-24-4422-24-21-2-22-4-1-122-2-2124-4-22-2-2-2000012-1-11-2221-111-1-1004-4000000000000-2-2220000000000-220011-1-10000000000000000000
χ8644-4-2-24-4422-24-21-2-22-4-1-122-2-2124-4-22-2-2-2000012-1-11-2221-111-1-100-4400000000000022-2-200000000002-200-1-1110000000000000000000
χ874-404440000-4-4-4444000000-4-4-40000000000004000-400000000000000000000000000000−2i22i200000000000000000000000000000−2i22i20000
χ884-404440000-4-4-4444000000-4-4-40000000000004000-4000000000000000000000000000002i2−2i2000000000000000000000000000002i2−2i20000
χ894-40-24400−2i32i32-4-4-24-200−2i32i3−2i32i32-42000000000000-20−2i32i3200000000000000000000000000000−2i22i200000000000000000000000000000i2−i26−600
χ904-40-24400−2i32i32-4-4-24-200−2i32i3−2i32i32-42000000000000-20−2i32i32000000000000000000000000000002i2−2i200000000000000000000000000000−i2i2−6600
χ914-40-244002i3−2i32-4-4-24-2002i3−2i32i3−2i32-42000000000000-202i3−2i3200000000000000000000000000000−2i22i200000000000000000000000000000i2−i2−6600
χ924-40-244002i3−2i32-4-4-24-2002i3−2i32i3−2i32-42000000000000-202i3−2i32000000000000000000000000000002i2−2i200000000000000000000000000000−i2i26−600
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
χ9588-8-4-4-48-844-4-4-422244-2-2-2-2222-44-44-4-2-240000-1-211-1-222-2211-1-1000000000000000000000000000000000000000000000000000000000
χ9688-8-4-4-4-8844-4-4-422244-2-2-2-22224-44-4422-40000-1-211-12-2-22-2-1-111000000000000000000000000000000000000000000000000000000000
χ978-8088-40000-84-88-4-400000044-8000000000000-40004000000000000000000000000000000000000000000000000000000000000000000
χ988-808-480000-8-84-4-48000000-844000000000000-40004000000000000000000000000000000000000000000000000000000000000000000
χ998-808-4-40000-844-42-40000004-24000006i−6i000002000-2000006i−6i00000000000000000000000000000000000000000000000000000000000
χ1008-808-4-40000-844-42-40000004-2400000−6i6i000002000-200000−6i6i00000000000000000000000000000000000000000000000000000000000
χ1018-80-48-400−4i34i344-8-4-4200−4i34i32i3−2i3-244000000000000202i3−2i3-2000000000000000000000000000000000000000000000000000000000000000000
χ1028-80-48-4004i3−4i344-8-4-42004i3−4i3−2i32i3-24400000000000020−2i32i3-2000000000000000000000000000000000000000000000000000000000000000000
χ1038-80-4-4800−4i34i34-842-4-4002i3−2i3−4i34i344-2000000000000202i3−2i3-2000000000000000000000000000000000000000000000000000000000000000000
χ1048-80-4-48004i3−4i34-842-4-400−2i32i34i3−4i344-200000000000020−2i32i3-2000000000000000000000000000000000000000000000000000000000000000000
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).