Finite Group Databasebeta

← Group #13171680

Character table — Group #13171680

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size112222222444444444488888888991212121212121212121216161616161618181818181818242424242424242424242424242424243636363636363636484848727272108108
order12333466633346661212123612121212121222244888242424241212121212122244466661212121224242424242424242424444661212126121212121228
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-11-1-1-1-1-1-1111111-1-11-1-11111-1-1-1-111-1-111-1-1-1-11-1-1-1-1-1-111-1-1-1-1111
χ311111111111111111111111111111-111-1111111111111-1-11-1-111-1-11111-1-111-1-111111-1-1-1-1-1-11-111-1-11-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1111-1-1
χ5111111111111111111111111111-1-111-111-111-1-11111111-1-11-1-1-1111-11-1111-11111-1-1-11-11-11-1-111-11-1-1-1-1
χ6111111111111111111111111111-1-11-111-11-1-111111111-11-1-11-1-111-11-1111-1111-1-111-1-11-11-11-11-11-11-1-1-1
χ7111111111111111111111111111-1-1-11-1-11-111-1-1111111-11-1-11-1-1-1-11-11-1-1-11-1-1-111-1-1-1-11-11-11-1-11-1-11-111
χ8111111111111111111111111111-1-1-1-11-1-11-1-1111111111-1-11-1-1-1-1-1-11-11-1-1-11-1-1-1-111-11-11-11-1-1-1-111-1-111
χ9111111111111-111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11-1
χ10111111111111-111111111-1-1-1111111-1-1-1111111-1-1-11-1-1-1-11-1-11111-1-1-1-1-1-111-1-11111-111-1-1-1-111-1-111-11-1
χ11111111111111-111111111-1-1-111111-1111-1-1-1-1-1-1-1-1-11-1-1-1-11-1-111-1-1111111-1-111-1-1-1-1-111-1-1-1-11-11111-1-11
χ12111111111111-111111111-1-1-111111-1-1-11111111-1-1-11-1-11111111-1-1-1-1-1-11111111111-1-1-111111-1-1-1-1-1-1-11
χ13111111111111-111111111-1-1-1111-1-111-1-1-11-1-111-1-1-11-1-11-1-11-1-1-1111-11-1-1-1-11-1-1-1-1111-111-11-1-111-1-111-11
χ14111111111111-111111111-1-1-1111-1-11-11-11-111-1-1-1-1-11-1-1-11-1-11-1-111-11-11-1-11-1-1-111-1-111-1-11-11-11-111-11-11
χ15111111111111-111111111-1-1-1111-1-1-11-11-11-1-111-1-1-11-1-1-11-1-11-1-1-1-11-11-111-1111-1-11111-1-11-11-1-11-11-111-1
χ16111111111111-111111111-1-1-1111-1-1-1-1111-111-1-1-1-1-11-1-11-1-11-1-1-1-1-1-11-11111-11111-1-11-111-11-1-1-1-11-1111-1
χ1722222-22222220222-2-2-222000-2-2-2220000000000000-20022-2-2-222000000000000000000022-2-2-200000000
χ1822222-22222220222-2-2-222000-2-2-2220000000000000-200-2-2-222220000000000000000000-2-222-200000000
χ1922222-22222220222-2-2-222000-2-2-2-2-20000000000000-2002-22-22-2-200000000000000000002-2-22200000000
χ2022222-22222220222-2-2-222000-2-2-2-2-20000000000000-200-2222-2-2-20000000000000000000-222-2200000000
χ212222-122-122-1-12-12-12-12-1-12-12-12-1002022020022-12-1-1-1-102002002-10-1022-10-1-1-100-1-10020-10-10-10-10-1000
χ222222-122-122-1-12-12-12-12-1-12-12-12-10020-220-200-2-2-12-1-1-1-10-200-2002-1010-22-101-1-1001100-201010-10101000
χ232222-122-122-1-12-12-12-12-1-12-12-12-100-202-2020022-12-1-1-1-10-200-200-210-102-210-11100-1-100-20101010-101000
χ242222-122-122-1-12-12-12-12-1-12-12-12-100-20-2-20-200-2-2-12-1-1-1-10200200-21010-2-21011100110020-10-101010-1000
χ252222-122-122-1-1-2-12-12-12-1-1-21-2-12-100202-20-200-2-21-21-11102002002-10-102-210111001100-20-10-10-10-101000
χ262222-122-122-1-1-2-12-12-12-1-1-21-2-12-10020-2-20200221-21-1110-200-2002-1010-2-210-11100-1-100201010-1010-1000
χ272222-122-122-1-1-2-12-12-12-1-1-21-2-12-100-20220-200-2-21-21-1110-200-200-210-1022-101-1-100110020101010-10-1000
χ282222-122-122-1-1-2-12-12-12-1-1-21-2-12-100-20-220200221-21-1110200200-21010-22-10-1-1-100-1-100-20-10-1010101000
χ29222-122-122-12-12-1-12-122-1-1-122-1-12002202202200-1-12-1-1-12002000-12-1020-12-10-1-1-1-100020-10-100-1-10-10000
χ30222-122-122-12-12-1-12-122-1-1-122-1-12002-202-20-2-200-1-12-1-1-1-200-2000-1210-20-1210-1-111000-2010100-11010000
χ31222-122-122-12-12-1-12-122-1-1-122-1-1200-220-2202200-1-12-1-1-1-200-20001-2-10201-2-1011-1-1000-20101001-1010000
χ32222-122-122-12-12-1-12-122-1-1-122-1-1200-2-20-2-20-2-200-1-12-1-1-120020001-210-201-210111100020-10-100110-10000
χ33222-122-122-12-1-2-1-12-122-1-11-2-2-1-1200220-2-20-2-20011-2-1112002000-12-10201-2101111000-20-10-100-1-1010000
χ34222-122-122-12-1-2-1-12-122-1-11-2-2-1-12002-20-220220011-2-111-200-2000-1210-201-2-1011-1-10002010100-110-10000
χ35222-122-122-12-1-2-1-12-122-1-11-2-2-1-1200-2202-20-2-20011-2-111-200-20001-2-1020-1210-1-11100020101001-10-10000
χ36222-122-122-12-1-2-1-12-122-1-11-2-2-1-1200-2-20220220011-2-11120020001-210-20-12-10-1-1-1-1000-20-10-10011010000
χ3722-122222-1-1-1222-1-122-1-1-122-12-1-122022022-1-1-1-12-1-1-1-1-100200-1-10022-1-1002200-1-1-1-12000000-10-1-100-100
χ3822-122222-1-1-1222-1-122-1-1-122-12-1-1220-2-20-2-211112-1-1-1-1-100200-1-100-2-21100-2-20011112000000-101100-100
χ3922-122222-1-1-1222-1-122-1-1-122-12-1-1-2-202-202-2-1-1112-1-1-1-1-100-20011002-2-11002-200-1-111-200000010-1100100
χ4022-122222-1-1-1222-1-122-1-1-122-12-1-1-2-20-220-2211-1-12-1-1-1-1-100-2001100-221-100-220011-1-1-2000000101-100100
χ4122-122222-1-1-12-22-1-122-1-1-1-2-212-1-1220220-2-21111-211-11100200-1-10022-1-100-2-2001111-2000000-10-1-100100
χ4222-122222-1-1-12-22-1-122-1-1-1-2-212-1-1220-2-2022-1-1-1-1-211-11100200-1-100-2-211002200-1-1-1-1-2000000-101100100
χ4322-122222-1-1-12-22-1-122-1-1-1-2-212-1-1-2-202-20-2211-1-1-211-11100-20011002-2-1100-220011-1-1200000010-1100-100
χ4422-122222-1-1-12-22-1-122-1-1-1-2-212-1-1-2-20-2202-2-1-111-211-11100-2001100-221-1002-200-1-1112000000101-100-100
χ454444-2-44-244-2-20-24-2-42-4-2-20002-420000000000000002000400-40000000000000000000000-202000000000
χ464444-2-44-244-2-20-24-2-42-4-2-20002-420000000000000002000-4004000000000000000000000020-2000000000
χ47444-24-4-244-24-20-2-242-4-4-2-200022-4000000000000000200400-40000000000000000000000-2020000000000
χ48444-24-4-244-24-20-2-242-4-4-2-200022-4000000000000000200-4004000000000000000000000020-20000000000
χ49444-2-24-2-24-2-2141-2-2-2-2411-2-241-2-20040040000001-2-21110000000-2-20000-2-2001100000000000010000000
χ50444-2-24-2-24-2-2141-2-2-2-2411-2-241-2-200-400-40000001-2-211100000002200002200-1-1000000000000-10000000
χ51444-2-24-2-24-2-21-41-2-2-2-241122-41-2-200400-4000000-1221-1-10000000-2-200002200-1-100000000000010000000
χ52444-2-24-2-24-2-21-41-2-2-2-241122-41-2-200-4004000000-1221-1-10000000220000-2-20011000000000000-10000000
χ5344-244-444-2-2-2404-2-2-4-42-2-2000-42244000000000000020000-400-2-200000000000000000000000200000000
χ5444-244-444-2-2-2404-2-2-4-42-2-2000-422-4-40000000000000200004002200000000000000000000000-200000000
χ5544-24-244-2-2-21-24-2-214-2-2114-2-2-2-210000400400-2-2-2-211110000000000-20-2000-20000110000000000100000
χ5644-24-244-2-2-21-24-2-214-2-2114-2-2-2-210000-400-40022-2-21111000000000020200020000-1-10000000000-100000
χ5744-24-244-2-2-21-2-4-2-214-2-211-422-2-210000400-4002222-11-1-10000000000-20-200020000-1-10000000000100000
χ5844-24-244-2-2-21-2-4-2-214-2-211-422-2-210000-400400-2-222-11-1-10000000000202000-20000110000000000-100000
χ5944-2-244-24-21-2-24-21-2-24-211-24-2-21-200040040-2-200-21-2111000000000-20-2000-200011000000000001000000
χ6044-2-244-24-21-2-24-21-2-24-211-24-2-21-2000-400-402200-21-21110000000002020002000-1-100000000000-1000000
χ6144-2-244-24-21-2-2-4-21-2-24-2112-42-21-2000400-4022002-121-1-1000000000-20-20002000-1-1000000000001000000
χ6244-2-244-24-21-2-2-4-21-2-24-2112-42-21-2000-40040-2-2002-121-1-1000000000202000-20001100000000000-1000000
χ634-44440-4-4-44440-4-4-40004-40000004-40000000000000000000004-400000000000000000000000000000000
χ644-44440-4-4-44440-4-4-40004-4000000-44000000000000000000000-4400000000000000000000000000000000
χ654-4-2440-4-42-2-240-422000-220000004-4000000i6−i6i6−i600000000000-22000000000000i6−i6i6−i60000000000000000
χ664-4-2440-4-42-2-240-422000-220000004-4000000−i6i6−i6i600000000000-22000000000000−i6i6−i6i60000000000000000
χ674-4-2440-4-42-2-240-422000-22000000-44000000i6−i6−i6i6000000000002-2000000000000i6−i6−i6i60000000000000000
χ684-4-2440-4-42-2-240-422000-22000000-44000000−i6i6i6−i6000000000002-2000000000000−i6i6i6−i60000000000000000
χ69888-4-4-8-4-48-4-4202-4-444-822000-244000000000000000-200000000000000000000000000000000000000000
χ7088-48-4-88-4-4-42-40-4-42-8442200044-2000000000000000-200000000000000000000000000000000000000000
χ7188-4-48-8-48-42-4-40-42-44-84220004-24000000000000000-200000000000000000000000000000000000000000
χ7288-4-4-48-4-4-42228222-4-4-4-1-1-4-4-4222000000000000222-1-1-1000000000000000000000000000000000000000
χ7388-4-4-48-4-4-4222-8222-4-4-4-1-1444222000000000000-2-2-2-111000000000000000000000000000000000000000
χ7488-4-4-4-8-4-4-42220222444-1-1000-2-2-20000000000000001−3i33i3000000000000000000000000000000000000000
χ7588-4-4-4-8-4-4-42220222444-1-1000-2-2-200000000000000013i3−3i3000000000000000000000000000000000000000
χ768-888-40-84-88-4-404-84000-44000000000000000000000000000000000000000000000000000000000000000
χ778-88-4804-8-8-48-4044-8000-44000000000000000000000000000000000000000000000000000000000000000
χ788-88-4-4044-8-4-420-2440002-200000000000000000000000000000000000000000−3i23i200000000000000000000
χ798-88-4-4044-8-4-420-2440002-2000000000000000000000000000000000000000003i2−3i200000000000000000000
χ808-8-48-40-844-42-4044-20002-200000000000000002i6−2i6000000000000000000000000000−i6i60000000000000000
χ818-8-48-40-844-42-4044-20002-20000000000000000−2i62i6000000000000000000000000000i6−i60000000000000000
χ828-8-4-4804-842-4-404-240002-2000000000000002i6−2i6000000000000000000000000000−i6i6000000000000000000
χ838-8-4-4804-842-4-404-240002-200000000000000−2i62i6000000000000000000000000000i6−i6000000000000000000
χ8416-16-8-8-808884440-4-4-4000-22000000000000000000000000000000000000000000000000000000000000000

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