Finite Group Databasebeta

← Group #13167830

Character table — Group #13167830

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size112222222444444444444668888888888888888888121212121212121212181824242424242424242424242424243636363636363648484848545454547272727272
order12333466633366681212121212243612121212242424242424242424242424242224668121224666666612121224242424222468126661224886661224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111111-1-111-111-11-1-1111111-1-11-1-1-1-111-1-1-1-1-11-1-11-1
χ3111111111111111111111111111111111111111111-1-11111111-1-1-1-11-1-1111111111-111-1-1-1-11-1-11-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-11-1-111111-1-1-1-1111-1-1-1-11111-1-1-1-11
χ5111111111111111111111-1-111111111111111111111111-1-1-1-1-111111111-111-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11
χ6111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-11111-111-1-1
χ7111111111111111111111-1-11111111111111111111-1-111-1-1-1-1-1-1-1-1-11-1-11-111-1-1-1-1-11-1-11-1-1-11-1-1111111-1-11-1
χ8111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111111
χ9111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-111111-111-111-1-11-1-1-1-1-11-111-1111-1-111-1-1-11-11-1
χ10111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-111-1-11-1-11-1-11111-1-1-1-1-1-111-11-1-11-11-1-111-1-1111
χ11111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-111-1-1-111-1111-1-11-1-1-1-111-1-1-11-11-11-1-1-11111-1-11
χ12111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-11111-11-1-11-11111-1-1-1-11-11-11-11-1-11111-1-11-11-1-1
χ13111111111111111-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11-1-1111-111-11-1-1-1-111111-11-11-1111-1-1-1-1111-11-1-1
χ14111111111111111-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11-1-1-1-11-1-11-1-1-111-1111111-1-1-11-1-11-1111-1-111-1-11
χ15111111111111111-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-1-1-1-1-111-111-1-1-1-11111-1-111-11-11-11-111-1-1-1-1111
χ16111111111111111-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11-1-111-11-1-11-1-111-11111-11-111-11-1-111-1-111-11-11-1
χ1722222-22222222220-2-2-2-2-22-222-2-2-2-200000000000000000220-2-22-2000000200-20000000020-20000-220000000
χ1822222-22222222220-2-2-2-2-22-222-2-2-2-200000000000000000220-2-2-22000000200-200000000-20200002-20000000
χ1922222-22222222220-2-2-2-2-2-2222-2-2-2-200000000000000000-2-20222-2000000-20020000000020-200002-20000000
χ2022222-22222222220-2-2-2-2-2-2222-2-2-2-200000000000000000-2-2022-22000000-200200000000-2020000-220000000
χ212222-12-122-1-122-1-12-12-1-1222-1-12-1-1-12-1-1-1222-1-1-1-1-1-100222-12-120000200-1-1-12-12-1-1-10220000-100-100000-1-100
χ222222-12-122-1-122-1-12-12-1-1222-1-12-1-1-12-1-1-1222-1-1-1-1-1-100-2-22-12-120000-2001-11-2-12-1-1-10-2-200001001000001100
χ232222-12-122-1-122-1-12-12-1-12-2-2-1-12-1-1-12-1-1-1222-1-1-1-1-1-10022-21-21-20000200-11-121-21110-2-20000-100-1000001100
χ242222-12-122-1-122-1-12-12-1-12-2-2-1-12-1-1-12-1-1-1222-1-1-1-1-1-100-2-2-21-21-20000-200111-21-21110220000100100000-1-100
χ252222-12-122-1-122-1-1-2-12-1-1222-1-12-1-1-1-2111-2-2-2111111002-22-1-2-120000200-1-11-2-1-211102-20000-100100000-1100
χ262222-12-122-1-122-1-1-2-12-1-1222-1-12-1-1-1-2111-2-2-211111100-222-1-2-120000-2001-1-12-1-21110-220000100-1000001-100
χ272222-12-122-1-122-1-1-2-12-1-12-2-2-1-12-1-1-1-2111-2-2-2111111002-2-2121-20000200-111-212-1-1-10-220000-1001000001-100
χ282222-12-122-1-122-1-1-2-12-1-12-2-2-1-12-1-1-1-2111-2-2-211111100-22-2121-20000-20011-1212-1-1-102-20000100-100000-1100
χ29222-12222-1-12-1-1-1222-1-1-1222-1-1-12-1-1-12-1-12-1-122-1-1-1-12200-1222-100220-1-10-100-1-12-1-120020000-1-100000-100-10
χ30222-12222-1-12-1-1-1222-1-1-1222-1-1-12-1-1-12-1-12-1-122-1-1-1-1-2-200-1222-100-2-20110-100-1-12-1-1-200-20000110000010010
χ31222-12222-1-12-1-1-1222-1-1-12-2-2-1-1-12-1-1-12-1-12-1-122-1-1-1-122001-2-2-2100220-1-1010011-211-200-20000-1-10000010010
χ32222-12222-1-12-1-1-1222-1-1-12-2-2-1-1-12-1-1-12-1-12-1-122-1-1-1-1-2-2001-2-2-2100-2-2011010011-211200200001100000-100-10
χ33222-12222-1-12-1-1-12-22-1-1-1222-1-1-12-1-11-211-211-2-211112-200-12-22-1002-20-110-100-11-211-20020000-1100000100-10
χ34222-12222-1-12-1-1-12-22-1-1-1222-1-1-12-1-11-211-211-2-21111-2200-12-22-100-2201-10-100-11-211200-200001-100000-10010
χ35222-12222-1-12-1-1-12-22-1-1-12-2-2-1-1-12-1-11-211-211-2-211112-2001-22-21002-20-1101001-12-1-1200-20000-1100000-10010
χ36222-12222-1-12-1-1-12-22-1-1-12-2-2-1-1-12-1-11-211-211-2-21111-22001-22-2100-2201-101001-12-1-1-200200001-100000100-10
χ3722-12222-122-1-1-12-122222-100-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-122220000022-1-1-122202-1000000000-12-1-1-1-1-100000000-1
χ3822-12222-122-1-1-12-122222-100-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-122-2-200000-2-2-1-1122-20-210000000001-211-1-11000000001
χ3922-12222-122-1-1-12-122222-100-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-2-22200000-2-211-1-2-2202-10000000001-21-111-1000000001
χ4022-12222-122-1-1-12-122222-100-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-20000022111-2-2-20-21000000000-12-1111100000000-1
χ4122-12222-122-1-1-12-1-22222-100-1-1-1-1-1-1-2-2-2-21111111112-22-20000022-11-12-220-21000000000-1-2-1-1-111000000001
χ4222-12222-122-1-1-12-1-22222-100-1-1-1-1-1-1-2-2-2-21111111112-2-2200000-2-2-1112-2-202-10000000001211-11-100000000-1
χ4322-12222-122-1-1-12-1-22222-100-1-1-1-1-1-1-2-2-2-2111111111-222-200000-2-21-1-1-2220-21000000000121-11-1100000000-1
χ4422-12222-122-1-1-12-1-22222-100-1-1-1-1-1-1-2-2-2-2111111111-22-2200000221-11-22-202-1000000000-1-2-111-1-1000000001
χ454444-2-4-244-2-244-2-202-422-44-4-2-2-4222000000000000000004-202-400000000-2002000000000000000000000000
χ464444-2-4-244-2-244-2-202-422-4-44-2-2-422200000000000000000-420-2400000000200-2000000000000000000000000
χ47444-24-444-2-24-2-2-240-4222-44-4-2-22-42200000000000000000-240-4200000000-2002000000000000000000000000
χ48444-24-444-2-24-2-2-240-4222-4-44-2-22-422000000000000000002-404-200000000200-2000000000000000000000000
χ49444-2-24-24-21-2-2-21-24-2-21144411-2-211-2-2114-2-2-2-211110000-2-24-2-2000000001001-2-21100000000000000000000
χ50444-2-24-24-21-2-2-21-24-2-2114-4-411-2-211-2-2114-2-2-2-21111000022-42200000000-100-122-1-100000000000000000000
χ51444-2-24-24-21-2-2-21-2-4-2-21144411-2-21122-1-1-42222-1-1-1-10000-2-2-4-2-200000000100122-1-100000000000000000000
χ52444-2-24-24-21-2-2-21-2-4-2-2114-4-411-2-21122-1-1-42222-1-1-1-100002242200000000-100-1-2-21100000000000000000000
χ53444-2-2-4-24-21-2-2-21-2022-1-1-44-41122-1-1003i−3i000003i3i−3i−3i0000-2-202200000000100-1003i−3i00000000000000000000
χ54444-2-2-4-24-21-2-2-21-2022-1-1-44-41122-1-100−3i3i00000−3i−3i3i3i0000-2-202200000000100-100−3i3i00000000000000000000
χ55444-2-2-4-24-21-2-2-21-2022-1-1-4-441122-1-1003i−3i000003i3i−3i−3i0000220-2-200000000-100100−3i3i00000000000000000000
χ56444-2-2-4-24-21-2-2-21-2022-1-1-4-441122-1-100−3i3i00000−3i−3i3i3i0000220-2-200000000-1001003i−3i00000000000000000000
χ5744-244-44-244-2-2-24-20-4-4-4-4200-2-2222200000000000000000000004-4000000000000000000-2020000000000000
χ5844-244-44-244-2-2-24-20-4-4-4-4200-2-222220000000000000000000000-4400000000000000000020-20000000000000
χ5944-24-24-2-24-21-2-2-214-24-2-2-20011-21114-2-2-2-2-2-21111110044000000000-200-20-2-20000000000001001000000000
χ6044-24-24-2-24-21-2-2-214-24-2-2-20011-21114-2-2-2-2-2-211111100-4-40000000002002022000000000000-100-1000000000
χ6144-24-24-2-24-21-2-2-21-4-24-2-2-20011-2111-4222222-1-1-1-1-1-1004-4000000000-200-2022000000000000100-1000000000
χ6244-24-24-2-24-21-2-2-21-4-24-2-2-20011-2111-4222222-1-1-1-1-1-100-4400000000020020-2-2000000000000-1001000000000
χ6344-2-2444-2-2-2-211-2-244-2-2-2-200111-211-24-2-2-211-2-2111144000000000-2-20-2-200000000000000000110000000000
χ6444-2-2444-2-2-2-211-2-244-2-2-2-200111-211-24-2-2-211-2-21111-4-40000000002202200000000000000000-1-10000000000
χ6544-2-2444-2-2-2-211-2-2-44-2-2-2-200111-2112-4222-1-122-1-1-1-14-4000000000-220-22000000000000000001-10000000000
χ6644-2-2444-2-2-2-211-2-2-44-2-2-2-200111-2112-4222-1-122-1-1-1-1-440000000002-202-200000000000000000-110000000000
χ674-44440-4-4-4444-4-4-4000000004-4000000000000000000000000000000000000000000000000000000022−2200000
χ684-44440-4-4-4444-4-4-4000000004-40000000000000000000000000000000000000000000000000000000−222200000
χ6988-48-4-8-4-48-42-4-4-4204-844400224-2-2-20000000000000000000000000000000000000000000000000000000000
χ7088-4-48-88-4-4-4-422-4-40-844440022-24-2-20000000000000000000000000000000000000000000000000000000000
χ7188-4-4-48-4-4-42222228-4-422-400-1-122-1-1-4-422-42222-1-1-1-1000000000000000000000000000000000000000000000
χ7288-4-4-48-4-4-4222222-8-4-422-400-1-122-1-144-2-24-2-2-2-21111000000000000000000000000000000000000000000000
χ7388-4-4-4-8-4-4-4222222044-2-2400-1-1-2-211006i−6i00000−3i−3i3i3i000000000000000000000000000000000000000000000
χ7488-4-4-4-8-4-4-4222222044-2-2400-1-1-2-21100−6i6i000003i3i−3i−3i000000000000000000000000000000000000000000000
χ758-888-404-8-8-4-48-84400000000-4400000000000000000000000000000000000000000000000000000000000000
χ768-88-480-8-84-48-444-800000000-4400000000000000000000000000000000000000000000000000000000000000
χ778-88-4-404-842-4-44-240006i−6i0002-2006i−6i0000000000000000000000000000000000000000000000000000000000
χ788-88-4-404-842-4-44-24000−6i6i0002-200−6i6i0000000000000000000000000000000000000000000000000000000000
χ798-8-4880-84-88-4-44-8400000000-4400000000000000000000000000000000000000000000000000000000000000
χ808-8-48-4044-8-42-444-2000000002-2000000000003i2−3i23i2−3i23i2−3i2000000000000000000000000000000000000000000000
χ818-8-48-4044-8-42-444-2000000002-200000000000−3i23i2−3i23i2−3i23i2000000000000000000000000000000000000000000000
χ828-8-4-480-844-4-42-244000000002-200000000032−320032−32−3232000000000000000000000000000000000000000000000
χ838-8-4-480-844-4-42-244000000002-2000000000−323200−323232−32000000000000000000000000000000000000000000000
χ848-8-4-4-40444222-2-2-20006i−6i000-1100−3i3i0000032−32−3i23i23ζ3−3ζ33ζ−3ζ000000000000000000000000000000000000000000000
χ858-8-4-4-40444222-2-2-20006i−6i000-1100−3i3i00000−32323i2−3i2−3ζ33ζ3−3ζ3ζ000000000000000000000000000000000000000000000
χ868-8-4-4-40444222-2-2-2000−6i6i000-11003i−3i0000032−323i2−3i2−3ζ3ζ−3ζ33ζ3000000000000000000000000000000000000000000000
χ878-8-4-4-40444222-2-2-2000−6i6i000-11003i−3i00000−3232−3i23i23ζ−3ζ3ζ3−3ζ3000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.