Finite Group Databasebeta

← Group #13167831

Character table — Group #13167831

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size112222222444444444444668888888888888888888121212121212121212181824242424242424242424242424243636363636363648484848545454547272727272
order1233346663336668121212121224361212121224242424242424242424242424222466812122466666661212122424242424446812666122488612121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111111-1-1-111-1111-1-11111111-1-1-1-1-1-111-1-1-1-1-111-1-1-1
χ3111111111111111111111111111111111111111111-1-11111111-1-11-1-11-1-111111111-1-111-1-1-11-1-11-1-1-1-1-1-111-1
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
χ6111111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-11111-1-111-1
χ7111111111111111111111-1-11111111111111111111-1-111-1-1-1-1-1-1-11-1-11-1-1-111-1-1-1-1-111-1-1-1-1-11-1-11111111-1-1-1
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
χ9111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1111111-111-11-1-11-1-1-1-11-11-11-1111-1-111-1-11-11-1-1
χ10111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-111-1-1-11-1-11-11111-1-1-1-11-1-11-11-1-11-11-1-1111-1-111
χ11111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-111-1-11-111-111-1-11-1-1-1-1-111-1-11-11-11-1-1-111-111-11
χ12111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-11111-1-11-1-111111-1-1-1-1-11-111-11-1-11111-1-1-11-11-1
χ13111111111111111-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11-1-11111-111-1-1-1-1-11111-11-111-1111-1-1-1-111-11-11-1
χ14111111111111111-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11-1-1-1-1-11-1-11-1-111-11111-111-1-11-1-11-1111-1-1-111-11
χ15111111111111111-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-1-1-1-11-111-11-1-1-1-111111-1-11-11-11-11-111-1-11-1-111
χ16111111111111111-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11-1-111-1-11-1-11-111-111111-11-11-11-1-111-1-1111-11-1-1
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
χ212222-122-12-12-1-1-122-12-1-1222-1-1-12-1-12-1-1-1222-1-1-1-1-1-122002-12-12000220-1-1-100-12-1-1-122000000-1-100000-1-1000
χ222222-122-12-12-1-1-122-12-1-1222-1-1-12-1-12-1-1-1222-1-1-1-1-1-1-2-2002-12-12000-2-2011-100-12-1-1-1-2-2000000110000011000
χ232222-122-12-12-1-1-122-12-1-12-2-2-1-1-12-1-12-1-1-1222-1-1-1-1-1-12200-21-21-2000220-1-11001-2111-2-2000000-1-10000011000
χ242222-122-12-12-1-1-122-12-1-12-2-2-1-1-12-1-12-1-1-1222-1-1-1-1-1-1-2-200-21-21-2000-2-20111001-2111220000001100000-1-1000
χ252222-122-12-12-1-1-12-2-12-1-1222-1-1-12-1-1-2111-2-2-21111112-2002-1-2-120002-20-11-100-1-21112-2000000-1100000-11000
χ262222-122-12-12-1-1-12-2-12-1-1222-1-1-12-1-1-2111-2-2-2111111-22002-1-2-12000-2201-1-100-1-2111-220000001-1000001-1000
χ272222-122-12-12-1-1-12-2-12-1-12-2-2-1-1-12-1-1-2111-2-2-21111112-200-2121-20002-20-1110012-1-1-1-22000000-11000001-1000
χ282222-122-12-12-1-1-12-2-12-1-12-2-2-1-1-12-1-1-2111-2-2-2111111-2200-2121-2000-2201-110012-1-1-12-20000001-100000-11000
χ29222-122-1222-1-1-12-122222-100-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1222200000222-1-1-1220-12000000000-12-1-1-1-1-100000000-1
χ30222-122-1222-1-1-12-122222-100-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-122-2-200000-2-2-2-1-112201-20000000001-211-1-11000000001
χ31222-122-1222-1-1-12-122222-100-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-2-22200000-2-2211-1-2-20-120000000001-21-111-1000000001
χ32222-122-1222-1-1-12-122222-100-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-20000022-2111-2-201-2000000000-12-1111100000000-1
χ33222-122-1222-1-1-12-1-22222-100-1-1-1-1-1-1-2-2-2-21111111112-22-200000222-11-12-201-2000000000-1-2-1-1-111000000001
χ34222-122-1222-1-1-12-1-22222-100-1-1-1-1-1-1-2-2-2-21111111112-2-2200000-2-2-2-1112-20-120000000001211-11-100000000-1
χ35222-122-1222-1-1-12-1-22222-100-1-1-1-1-1-1-2-2-2-2111111111-222-200000-2-221-1-1-2201-2000000000121-11-1100000000-1
χ36222-122-1222-1-1-12-1-22222-100-1-1-1-1-1-1-2-2-2-2111111111-22-220000022-21-11-220-12000000000-1-2-111-1-1000000001
χ3722-122222-1-1-122-1-122-1-1-1222-1-12-1-1-1-12-1-12-1-122-1-1-1-10022-1222-100-100200-12-1-1-12-1-10022000-100-1000000-1-10
χ3822-122222-1-1-122-1-122-1-1-1222-1-12-1-1-1-12-1-12-1-122-1-1-1-100-2-2-1222-100100-200-1-21-1-12-1-100-2-20001001000000110
χ3922-122222-1-1-122-1-122-1-1-12-2-2-1-12-1-1-1-12-1-12-1-122-1-1-1-100221-2-2-2100-10020012-111-21100-2-2000-100-1000000110
χ4022-122222-1-1-122-1-122-1-1-12-2-2-1-12-1-1-1-12-1-12-1-122-1-1-1-100-2-21-2-2-2100100-2001-2111-21100220001001000000-1-10
χ4122-122222-1-1-122-1-1-22-1-1-1222-1-12-1-1-11-211-211-2-21111002-2-12-22-100-100200-1-21-11-211002-2000-1001000000-110
χ4222-122222-1-1-122-1-1-22-1-1-1222-1-12-1-1-11-211-211-2-2111100-22-12-22-100100-200-12-1-11-21100-22000100-10000001-10
χ4322-122222-1-1-122-1-1-22-1-1-12-2-2-1-12-1-1-11-211-211-2-21111002-21-22-2100-1002001-211-12-1-100-22000-10010000001-10
χ4422-122222-1-1-122-1-1-22-1-1-12-2-2-1-12-1-1-11-211-211-2-2111100-221-22-2100100-20012-11-12-1-1002-2000100-1000000-110
χ454444-2-44-24-24-2-2-2402-422-44-4-2-22-422000000000000000004-202-400000000-2002000000000000000000000000
χ464444-2-44-24-24-2-2-2402-422-4-44-2-22-42200000000000000000-420-2400000000200-2000000000000000000000000
χ47444-24-4-2444-2-2-24-20-4-4-4-4200-2-2222200000000000000000000004-4000000000000000000-2020000000000000
χ48444-24-4-2444-2-2-24-20-4-4-4-4200-2-222220000000000000000000000-4400000000000000000020-20000000000000
χ49444-2-24-2-24-2-211-2-24-24-2-2-200111-2114-2-2-2-2-2-2111111440000000000-2-20-2-20000000000000000110000000000
χ50444-2-24-2-24-2-211-2-24-24-2-2-200111-2114-2-2-2-2-2-2111111-4-40000000000220220000000000000000-1-10000000000
χ51444-2-24-2-24-2-211-2-2-4-24-2-2-200111-211-4222222-1-1-1-1-1-14-40000000000-220-2200000000000000001-10000000000
χ52444-2-24-2-24-2-211-2-2-4-24-2-2-200111-211-4222222-1-1-1-1-1-1-4400000000002-202-20000000000000000-110000000000
χ5344-244-444-2-2-244-2-20-4222-44-4-2-2-422200000000000000000-240-4200000000-2002000000000000000000000000
χ5444-244-444-2-2-244-2-20-4222-4-44-2-2-4222000000000000000002-404-200000000200-2000000000000000000000000
χ5544-24-244-2-21-2-2-21-24-2-21144411-2-211-2-2114-2-2-2-211110000-2-24-2-2000000001001-2-21100000000000000000000
χ5644-24-244-2-21-2-2-21-24-2-2114-4-411-2-211-2-2114-2-2-2-21111000022-42200000000-100-122-1-100000000000000000000
χ5744-24-244-2-21-2-2-21-2-4-2-21144411-2-21122-1-1-42222-1-1-1-10000-2-2-4-2-200000000100122-1-100000000000000000000
χ5844-24-244-2-21-2-2-21-2-4-2-2114-4-411-2-21122-1-1-42222-1-1-1-100002242200000000-100-1-2-21100000000000000000000
χ5944-24-2-44-2-21-2-2-21-2022-1-1-44-41122-1-1003i−3i000003i3i−3i−3i0000-2-202200000000100-1003i−3i00000000000000000000
χ6044-24-2-44-2-21-2-2-21-2022-1-1-44-41122-1-100−3i3i00000−3i−3i3i3i0000-2-202200000000100-100−3i3i00000000000000000000
χ6144-24-2-44-2-21-2-2-21-2022-1-1-4-441122-1-1003i−3i000003i3i−3i−3i0000220-2-200000000-100100−3i3i00000000000000000000
χ6244-24-2-44-2-21-2-2-21-2022-1-1-4-441122-1-100−3i3i00000−3i−3i3i3i0000220-2-200000000-1001003i−3i00000000000000000000
χ6344-2-244-24-2-21-2-2-2144-2-2-2-20011-2111-24-2-2-211-2-2111100440000000-200-2000-2-20000000000001001000000000
χ6444-2-244-24-2-21-2-2-2144-2-2-2-20011-2111-24-2-2-211-2-2111100-4-40000000200200022000000000000-100-1000000000
χ6544-2-244-24-2-21-2-2-21-44-2-2-2-20011-21112-4222-1-122-1-1-1-1004-40000000-200-200022000000000000100-1000000000
χ6644-2-244-24-2-21-2-2-21-44-2-2-2-20011-21112-4222-1-122-1-1-1-100-4400000002002000-2-2000000000000-1001000000000
χ674-44440-4-4-4444-4-4-4000000004-400000000000000000000000000000000000000000000000000000002i2−2i200000
χ684-44440-4-4-4444-4-4-4000000004-40000000000000000000000000000000000000000000000000000000−2i22i200000
χ69888-4-4-8-4-48-4-422-4-404-84440022-24-2-20000000000000000000000000000000000000000000000000000000000
χ7088-4-48-8-48-4-42-4-4-420-8444400224-2-2-20000000000000000000000000000000000000000000000000000000000
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
χ758-888-40-84-8-48-444-800000000-4400000000000000000000000000000000000000000000000000000000000000
χ768-88-4804-8-88-4-44-8400000000-4400000000000000000000000000000000000000000000000000000000000000
χ778-88-4-4044-8-4-42-244000000002-20000000000032−3232−3232−32000000000000000000000000000000000000000000000
χ788-88-4-4044-8-4-42-244000000002-200000000000−3232−3232−3232000000000000000000000000000000000000000000000
χ798-8-4880-8-84-4-48-84400000000-4400000000000000000000000000000000000000000000000000000000000000
χ808-8-48-40-8442-4-44-240006i−6i0002-2006i−6i0000000000000000000000000000000000000000000000000000000000
χ818-8-48-40-8442-4-44-24000−6i6i0002-200−6i6i0000000000000000000000000000000000000000000000000000000000
χ828-8-4-4804-84-42-444-2000000002-20000000003i2−3i2003i2−3i2−3i23i2000000000000000000000000000000000000000000000
χ838-8-4-4804-84-42-444-2000000002-2000000000−3i23i200−3i23i23i2−3i2000000000000000000000000000000000000000000000
χ848-8-4-4-40444222-2-2-20006i−6i000-1100−3i3i000003i2−3i2−3232−3ζ33ζ33ζ−3ζ000000000000000000000000000000000000000000000
χ858-8-4-4-40444222-2-2-20006i−6i000-1100−3i3i00000−3i23i232−323ζ3−3ζ3−3ζ3ζ000000000000000000000000000000000000000000000
χ868-8-4-4-40444222-2-2-2000−6i6i000-11003i−3i000003i2−3i232−32−3ζ3ζ3ζ3−3ζ3000000000000000000000000000000000000000000000
χ878-8-4-4-40444222-2-2-2000−6i6i000-11003i−3i00000−3i23i2−32323ζ−3ζ−3ζ33ζ3000000000000000000000000000000000000000000000

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