Finite Group Databasebeta

← Group #13170551

Character table — Group #13170551

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size11222222222444444444444444444444666688888888888888121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636363636363654547272108
order1223334466633366666666121212121212121212122244366666121212121212121224446666661212121212121212121266666121212121212121212121222246666668812128824248
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1111111-1-111-1-1111111-111-1-1-11111-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ511111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-111-1-111-1-111111-1-111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1
χ611111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11-1-1111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11
χ711111111111111111111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-11
χ811111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1
χ911-1111-11111111-1-1-1-1-11111-1-11-111-1-111-11-11-1-1-1-111-11-111-1-11-11-11-11-1111-1-1-11-111-1-111-111-11-11-1-1-111-1-11-11-11111-1-11-1-1-1-1-11-11
χ1011-1111-11111111-1-1-1-1-11111-1-11-111-1-111-11-11-1-1-1-111-11-111-1-11-1-111-11-1111-1-1-11-1-1-11111-111-1-111-1-1-1-1-1111-1-11-1-111-1-1-111111-11-1
χ1111-1111-11111111-1-1-1-1-11111-1-11-111-1-111-11-11-1-1-1-111-11-111-1-1-111-11-11-1-1-11-1111-111-1-1-11-1-1-111-11-11111-1-1-111-111-1-111-11-1-111-11-1
χ1211-1111-11111111-1-1-1-1-11111-1-11-111-1-111-11-11-1-1-1-111-11-111-1-1-11-111-11-1-1-11-1111-1-1-111-11-1-1-11-111-111-1-111-11-11-1-1-1-1111-111-1-11-11
χ1311-1111-11111111-1-1-1-1-11111-1-11-111-1-11-11-111-1-1-1-111-11-111-1-11-11-1-11-1111-11-1-1-1111-1-11-1111-11-1-11-1-111-1-1-11-11-1-1-1-1111-111111-1-1
χ1411-1111-11111111-1-1-1-1-11111-1-11-111-1-11-11-111-1-1-1-111-11-111-1-11-1-11-11-1111-11-1-1-11-1-1111-1111-1-11-11-1-1-1-111-111-111-1-111-11-1-1-1-1-111
χ1511-1111-11111111-1-1-1-1-11111-1-11-111-1-11-11-111-1-1-1-111-11-111-1-1-111-1-11-11-1-1-1111-1111-1-1-1-11-1-111-1-111111-1-11-1-11-1-111-1-1-1111-1-1-111
χ1611-1111-11111111-1-1-1-1-11111-1-11-111-1-11-11-111-1-1-1-111-11-111-1-1-11-11-11-11-1-1-1111-11-1-111-1-11-1-11-11-1111-1-1111-11-11111-1-11-1-1-1111-1-1
χ17222222-2-222222222222222-2-2-2-2-2-2-2-2-2-22-2-22222222-2-2-2-2-2-2-2-200002-22-200-2200-22000002-200000-220000000000000000000000000
χ18222222-2-222222222222222-2-2-2-2-2-2-2-2-2-2-222-2222222-2-2-2-2-2-2-2-20000-22-22002-2002-200000-22000002-20000000000000000000000000
χ1922222-122-1222-1-122-122-1-12-1-1222-1-1-1-122222-1-1-1-1-1-1-1-122-1-1-1-1220022-1-1-1-1-1-1-1-12200002-1-1-1-1200-1-1-1-10000220000-1-1-1-1000000000
χ2022222-122-1222-1-122-122-1-12-1-1222-1-1-1-122222-1-1-1-1-1-1-1-122-1-1-1-1-2-20022-1-111-1-111220000-2-1-111-200-1-1110000-2-200001111000000000
χ2122222-122-1222-1-122-122-1-12-1-1222-1-1-1-12-2-2-2-2-1-1-1-1-1-1-1-122-1-1-1-12200-2-211-1-111-1-1-2-20000211-1-120011-1-10000-2-200001111000000000
χ2222222-122-1222-1-122-122-1-12-1-1222-1-1-1-12-2-2-2-2-1-1-1-1-1-1-1-122-1-1-1-1-2-200-2-211111111-2-20000-21111-20011110000220000-1-1-1-1000000000
χ2322222-1-2-2-1222-1-122-122-1-1211-2-2-21111-22-2-22-1-1-1-1-1-111-2-2111100002-2-11−i3i31-1−i3i3-2200000-11−i3i30001-1−i3i30000000000−i3i3−i3i3000000000
χ2422222-1-2-2-1222-1-122-122-1-1211-2-2-21111-22-2-22-1-1-1-1-1-111-2-2111100002-2-11i3−i31-1i3−i3-2200000-11i3−i30001-1i3−i30000000000i3−i3i3−i3000000000
χ2522222-1-2-2-1222-1-122-122-1-1211-2-2-21111-2-222-2-1-1-1-1-1-111-2-211110000-221-1−i3i3-11−i3i32-2000001-1−i3i3000-11−i3i30000000000i3−i3i3−i3000000000
χ2622222-1-2-2-1222-1-122-122-1-1211-2-2-21111-2-222-2-1-1-1-1-1-111-2-211110000-221-1i3−i3-11i3−i32-2000001-1i3−i3000-11i3−i30000000000−i3i3−i3i3000000000
χ272222-122222-1-12-12-12-1-12-1-1222-1-1-1-12222222-12-1-1-1-12-1-1-1-1-1-1-10022-1-122002200-1-1-1-1-1-10-1-100022-1-100-1-1-1-10022-1-1000000-1-100000
χ282222-122222-1-12-12-12-1-12-1-1222-1-1-1-12222222-12-1-1-1-12-1-1-1-1-1-1-100-2-2-1-122002200-1-111110-1-1000-2-2-1-100111100-2-2110000001100000
χ292222-122222-1-12-12-12-1-12-1-1222-1-1-1-1222-2-2-2-2-12-1-1-1-12-1-1-1-1-1-1-1002211-2-200-2-20011-1-1-1-1011000221100-1-1-1-100-2-2110000001100000
χ302222-122222-1-12-12-12-1-12-1-1222-1-1-1-1222-2-2-2-2-12-1-1-1-12-1-1-1-1-1-1-100-2-211-2-200-2-200111111011000-2-2110011110022-1-1000000-1-100000
χ312222-12-2-222-1-12-12-12-1-12-1-1-2-2-21111-2-2-22-2-22-12-1-1-1-1-211111110000-112-200-22001-1−i3i3−i3i30-11000001-100−i3i3−i3i30000−i3i3000000−i3i300000
χ322222-12-2-222-1-12-12-12-1-12-1-1-2-2-21111-2-2-22-2-22-12-1-1-1-1-211111110000-112-200-22001-1i3−i3i3−i30-11000001-100i3−i3i3−i30000i3−i3000000i3−i300000
χ332222-12-2-222-1-12-12-12-1-12-1-1-2-2-21111-2-2-2-222-2-12-1-1-1-1-2111111100001-1-22002-200-11−i3i3−i3i301-100000-1100−i3i3−i3i30000i3−i3000000i3−i300000
χ342222-12-2-222-1-12-12-12-1-12-1-1-2-2-21111-2-2-2-222-2-12-1-1-1-1-2111111100001-1-22002-200-11i3−i3i3−i301-100000-1100i3−i3i3−i30000−i3i3000000−i3i300000
χ35222-122222-12-1-12-122-1-1-12-122-12222-1-1-10000-1-12-1-1-1-12-1-1-1-1-1-122220000220022002222-100-1-1-1-1-100-1-1-1-1-1-10000000000220000-1-10
χ36222-122222-12-1-12-122-1-1-12-122-12222-1-1-10000-1-12-1-1-1-12-1-1-1-1-1-122-2-2000022002200-2-2-2-2-100-1-1-11100-1-111110000000000-2-20000110
χ37222-122222-12-1-12-122-1-1-12-122-12222-1-1-10000-1-12-1-1-1-12-1-1-1-1-1-1-2-2220000-2-200-2-2002222100111-1-10011-1-1-1-10000000000-2-20000110
χ38222-122222-12-1-12-122-1-1-12-122-12222-1-1-10000-1-12-1-1-1-12-1-1-1-1-1-1-2-2-2-20000-2-200-2-200-2-2-2-210011111001111110000000000220000-1-10
χ3922-22222-2222222-2-2-2-2-2222-222-22-2-222-222-2-22-2-2-2-22-22-22-2-2220000222200-2-200-2-2000002200000-2-20000000000000000000000000
χ4022-22222-2222222-2-2-2-2-2222-222-22-2-222-2-2-2222-2-2-2-22-22-22-2-2220000-2-2-2-20022002200000-2-200000220000000000000000000000000
χ4122-222-12-2-1222-1-1-2-21-2-2-1-121-12-2211-1-1-222-2-2-11111-11-1-2211-1-1000022-1-1−i3i311i3−i3-2-200000-1-1−i3i300011i3−i30000000000−i3i3i3−i3000000000
χ4222-222-12-2-1222-1-1-2-21-2-2-1-121-12-2211-1-1-222-2-2-11111-11-1-2211-1-1000022-1-1i3−i311−i3i3-2-200000-1-1i3−i300011−i3i30000000000i3−i3−i3i3000000000
χ4322-222-12-2-1222-1-1-2-21-2-2-1-121-12-2211-1-1-2-2-222-11111-11-1-2211-1-10000-2-211−i3i3-1-1i3−i3220000011−i3i3000-1-1i3−i30000000000i3−i3−i3i3000000000
χ4422-222-12-2-1222-1-1-2-21-2-2-1-121-12-2211-1-1-2-2-222-11111-11-1-2211-1-10000-2-211i3−i3-1-1−i3i3220000011i3−i3000-1-1−i3i30000000000−i3i3i3−i3000000000
χ4522-222-1-22-1222-1-1-2-21-2-2-1-12-11-22-2-1-11122-22-2-11111-1-112-2-1-1112-2002-2-11-1-1-11112-200002-11-1-1-200-111100002-20000-1-111000000000
χ4622-222-1-22-1222-1-1-2-21-2-2-1-12-11-22-2-1-11122-22-2-11111-1-112-2-1-111-22002-2-1111-11-1-12-20000-2-1111200-11-1-10000-22000011-1-1000000000
χ4722-222-1-22-1222-1-1-2-21-2-2-1-12-11-22-2-1-1112-22-22-11111-1-112-2-1-1112-200-221-1-1-11-111-22000021-1-1-1-2001-1110000-22000011-1-1000000000
χ4822-222-1-22-1222-1-1-2-21-2-2-1-12-11-22-2-1-1112-22-22-11111-1-112-2-1-111-2200-221-1111-1-1-1-220000-21-1112001-1-1-100002-20000-1-111000000000
χ4922-22-122-222-1-12-1-21-2112-1-1-2221-11122-222-2-2-1-2111-1-2-11-111-1-10000-1-12200-2-20011−i3i3i3−i30-1-1000001100−i3i3i3−i30000−i3i3000000i3−i300000
χ5022-22-122-222-1-12-1-21-2112-1-1-2221-11122-222-2-2-1-2111-1-2-11-111-1-10000-1-12200-2-20011i3−i3−i3i30-1-1000001100i3−i3−i3i30000i3−i3000000−i3i300000
χ5122-22-122-222-1-12-1-21-2112-1-1-2221-11122-2-2-222-1-2111-1-2-11-111-1-1000011-2-2002200-1-1−i3i3i3−i301100000-1-100−i3i3i3−i30000i3−i3000000−i3i300000
χ5222-22-122-222-1-12-1-21-2112-1-1-2221-11122-2-2-222-1-2111-1-2-11-111-1-1000011-2-2002200-1-1i3−i3−i3i301100000-1-100i3−i3−i3i30000−i3i3000000i3−i300000
χ5322-22-12-2222-1-12-1-21-2112-1-12-2-2-11-1-1-2-222-22-2-1-2111-121-11-1-111002-2-112-2002-200-11-1-1110-110002-2-1100-1-111002-2-1-10000001100000
χ5422-22-12-2222-1-12-1-21-2112-1-12-2-2-11-1-1-2-222-22-2-1-2111-121-11-1-11100-22-112-2002-200-1111-1-10-11000-22-110011-1-100-2211000000-1-100000
χ5522-22-12-2222-1-12-1-21-2112-1-12-2-2-11-1-1-2-22-22-22-1-2111-121-11-1-111002-21-1-2200-22001-1-1-11101-10002-21-100-1-11100-2211000000-1-100000
χ5622-22-12-2222-1-12-1-21-2112-1-12-2-2-11-1-1-2-22-22-22-1-2111-121-11-1-11100-221-1-2200-22001-111-1-101-1000-221-10011-1-1002-2-1-10000001100000
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χ5822-2-122-222-12-1-121-2-211-12-12-212-22211-10000-11-211-1-1-2-11-1-1112-2-2200002200-2-200-2-222-100-1-111-1001111-1-10000000000-2200001-10
χ5922-2-122-222-12-1-121-2-211-12-12-212-22211-10000-11-211-1-1-2-11-1-111-222-20000-2-200220022-2-210011-1-1100-1-1-1-1110000000000-2200001-10
χ6022-2-122-222-12-1-121-2-211-12-12-212-22211-10000-11-211-1-1-2-11-1-111-22-220000-2-2002200-2-22210011-11-100-1-111-1-100000000002-20000-110
χ614444-2-244-24-2-2-214-2-2-2-2-21-2-2-24-2-211-2-2444441-21111-21-2-211110000-2-2-2-200-2-200-2-2000001100000110000000000000000000000000
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χ8044-4-24-24-4-2-24-21-22-42221-2-22-2-2-442211200001-12-1-11-1-22-2-1-111000000002i3−2i300−2i32i3000000000−i3i300000i3−i300000000000000000000000
χ8144-4-24-2-44-2-24-21-22-42221-2-2-2224-4-2-2-1-1-200001-12-1-1112-2211-1-14-4000000-2-20022000000-2001120000-1-100000000000000000000000
χ8244-4-24-2-44-2-24-21-22-42221-2-2-2224-4-2-2-1-1-200001-12-1-1112-2211-1-1-440000002200-2-2000000200-1-1-200001100000000000000000000000
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χ874-4044400-4-4-444400000-4-4-40000000000000040000-40000000000000000000000000000000000000000000000000000000000−2i22i2000
χ884-4044400-4-4-444400000-4-4-40000000000000040000-400000000000000000000000000000000000000000000000000000000002i2−2i2000
χ89888-4-4-488-4-4-4222-4-4-422222-4-4-4-4-42222-40000-122-1-1-12222-1-1-1-10000000000000000000000000000000000000000000000000000000
χ90888-4-4-4-8-8-4-4-4222-4-4-42222244444-2-2-2-240000-122-1-1-1-2-2-2-211110000000000000000000000000000000000000000000000000000000
χ9188-8-4-4-48-8-4-4-4222444-2-22224-4-44-4-2-22240000-1-2-211-1-22-2211-1-10000000000000000000000000000000000000000000000000000000
χ9288-8-4-4-4-88-4-4-4222444-2-2222-444-4422-2-2-40000-1-2-211-12-22-2-1-1110000000000000000000000000000000000000000000000000000000
χ938-8088-4004-8-88-4-40000044-800000000000000-400004000000000000000000000000000000000000000000000000000000000000000
χ948-808-4800-8-84-48-400000-84400000000000000-400004000000000000000000000000000000000000000000000000000000000000000
χ958-808-4-4004-84-4-42000004-24000006i−6i000000020000-200006i−6i000000000000000000000000000000000000000000000000000000000
χ968-808-4-4004-84-4-42000004-2400000−6i6i000000020000-20000−6i6i000000000000000000000000000000000000000000000000000000000
χ978-80-48800-84-8-4-48000004-8400000000000000-400004000000000000000000000000000000000000000000000000000000000000000
χ988-80-48-40044-8-42-400000-24400000006i−6i0000020000-20000006i−6i0000000000000000000000000000000000000000000000000000000
χ998-80-48-40044-8-42-400000-2440000000−6i6i0000020000-2000000−6i6i0000000000000000000000000000000000000000000000000000000
χ1008-80-4-4800-8442-4-40006-644-2000000000000002006-6-2000000000000000000000000000000000000000000000000000000000000000
χ1018-80-4-4800-8442-4-4000-6644-200000000000000200-66-2000000000000000000000000000000000000000000000000000000000000000
χ1028-80-4-4-4004442220006-6-2-2-2000006i−6i6i−6i00000-100-3310000−3i3i−3i3i0000000000000000000000000000000000000000000000000000000
χ1038-80-4-4-4004442220006-6-2-2-200000−6i6i−6i6i00000-100-33100003i−3i3i−3i0000000000000000000000000000000000000000000000000000000
χ1048-80-4-4-400444222000-66-2-2-2000006i−6i−6i6i00000-1003-310000−3i3i3i−3i0000000000000000000000000000000000000000000000000000000
χ1058-80-4-4-400444222000-66-2-2-200000−6i6i6i−6i00000-1003-3100003i−3i−3i3i0000000000000000000000000000000000000000000000000000000

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