Finite Group Databasebeta

← Group #13156234

Character table — Group #13156234

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size112222222222244444444444444444444888888888888881212181824242424242424242424242424242424242424242424242424243636363636727272727272108108
order12233344666663336666666661212121212121212366661212121212121212122488226666666666666666666612121212824242424882424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-111
χ31111111111111111111111111111111111111111111111111-1-11-11111-1-111-1-1111111-1-1-1-11111-1-1-1-1-11-111-1-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1111-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-11-1-111-1-1
χ511111111111111111111111111111111111111111111111-1-11111-1-111111111-1-111111111-1-1-1-111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1
χ711111111111111111111111111111111111111111111111-1-1-1-11-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111
χ811111111111111111111111111111111111111111111111-1-1-1-1-11-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-1-111
χ9222222-2-222222222222222222-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000002i−2i
χ10222222-2-222222222222222222-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000−2i2i
χ1122222-122-1-1-1222-1-122-1-1-1-1-1-12-12222-122-12-1-1-1-1-1-1-12-1-1-1-1002222002222-1-1-1-100-1-1-1-1-1-1-1-100002-1-1-1-100000000
χ1222222-122-1-1-1222-1-122-1-1-1-1-1-12-12222-122-12-1-1-1-1-1-1-12-1-1-1-10022-2-200-2-2-2-21111001111111100002-1-1-1-100000000
χ1322222-122-1-1-1222-1-122-1-1-1-1-1-12-12222-122-12-1-1-1-1-1-1-12-1-1-1-100-2-22-20022-2-2-1-11100-1-1-1-111110000-2111100000000
χ1422222-122-1-1-1222-1-122-1-1-1-1-1-12-12222-122-12-1-1-1-1-1-1-12-1-1-1-100-2-2-2200-2-22211-1-1001111-1-1-1-10000-2111100000000
χ152222-12222222-1-12-12-122-1-12-1-122-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-12200022-100-1-10022-1-10000-1-1-1-12-1-1-1000000200-1-100
χ162222-12222222-1-12-12-122-1-12-1-122-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-122000-22-1001100-2-2-1-1000011112-1-1-1000000-2001100
χ172222-12222222-1-12-12-122-1-12-1-122-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-2-20002-2100-1-10022110000-1-1-1-1-2111000000-2001100
χ182222-12222222-1-12-12-122-1-12-1-122-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-2-2000-2-21001100-2-21100001111-2111000000200-1-100
χ19222-12222222-12-1-12-12-1-122-12-12-12-1-12-12-1-1-1-1-1-1-122-1-1-1-1-1220020-12-1-1002200-1-1-1-1-1-10000-12-1-10000020-1-10000
χ20222-12222222-12-1-12-12-1-122-12-12-12-1-12-12-1-1-1-1-1-1-122-1-1-1-1-12200-20-121100-2-200-1-111110000-12-1-100000-20110000
χ21222-12222222-12-1-12-12-1-122-12-12-12-1-12-12-1-1-1-1-1-1-122-1-1-1-1-1-2-200201-2-1-100220011-1-1-1-100001-21100000-20110000
χ22222-12222222-12-1-12-12-1-122-12-12-12-1-12-12-1-1-1-1-1-1-122-1-1-1-1-1-2-200-201-21100-2-20011111100001-2110000020-1-10000
χ2322-22222-2-2-2222222-2-2-2-2-2-22222-2-2-2-2-2222-2-2-222-22-2222-2-22-2000022000000002200000000-2-2-2-20000000000000
χ2422-22222-2-2-2222222-2-2-2-2-2-22222-2-2-2-2-2222-2-2-222-22-2222-2-2-220000-2-200000000-2-20000000022220000000000000
χ2522-2222-22-2-2222222-2-2-2-2-2-2222-222222-2-22-2-2-22-22-22-2-2-222002200000000000000000000000000-222-2-200000000
χ2622-2222-22-2-2222222-2-2-2-2-2-2222-222222-2-22-2-2-22-22-22-2-2-22200-2-2000000000000000000000000002-2-22200000000
χ2722-222-1-2211-1222-1-1-2-21111-1-1212222-1-2-2-1-211-11-11-1-211-1-1002200000000−i3i3−i3i300−i3−i3i3i3−i3−i3i3i30000-2-1-11100000000
χ2822-222-1-2211-1222-1-1-2-21111-1-1212222-1-2-2-1-211-11-11-1-211-1-1002200000000i3−i3i3−i300i3i3−i3−i3i3i3−i3−i30000-2-1-11100000000
χ2922-222-1-2211-1222-1-1-2-21111-1-1212222-1-2-2-1-211-11-11-1-211-1-100-2-200000000−i3i3i3−i300−i3−i3i3i3i3i3−i3−i30000211-1-100000000
χ3022-222-1-2211-1222-1-1-2-21111-1-1212222-1-2-2-1-211-11-11-1-211-1-100-2-200000000i3−i3−i3i300i3i3−i3−i3−i3−i3i3i30000211-1-100000000
χ3122-22-122-2-2-222-1-12-1-21-2-2112-1-12-2111-22-1-1111-12-2-11-1-1-1112-200002-100−i3i30000-1-10000−i3i3−i3i3-2111000000000−i3i300
χ3222-22-122-2-2-222-1-12-1-21-2-2112-1-12-2111-22-1-1111-12-2-11-1-1-1112-200002-100i3−i30000-1-10000i3−i3i3−i3-2111000000000i3−i300
χ3322-22-122-2-2-222-1-12-1-21-2-2112-1-12-2111-22-1-1111-12-2-11-1-1-111-220000-2100−i3i30000110000−i3i3−i3i32-1-1-1000000000i3−i300
χ3422-22-122-2-2-222-1-12-1-21-2-2112-1-12-2111-22-1-1111-12-2-11-1-1-111-220000-2100i3−i30000110000i3−i3i3−i32-1-1-1000000000−i3i300
χ3522-2-1222-2-2-22-12-1-121-211-2-2-12-121-211-2-12-1111-1-112-2-1-1-1112-20000-12−i3i3000000-1-1−i3i3−i3i300001-2110000000−i3i30000
χ3622-2-1222-2-2-22-12-1-121-211-2-2-12-121-211-2-12-1111-1-112-2-1-1-1112-20000-12i3−i3000000-1-1i3−i3i3−i300001-2110000000i3−i30000
χ3722-2-1222-2-2-22-12-1-121-211-2-2-12-121-211-2-12-1111-1-112-2-1-1-111-2200001-2−i3i300000011−i3i3−i3i30000-12-1-10000000i3−i30000
χ3822-2-1222-2-2-22-12-1-121-211-2-2-12-121-211-2-12-1111-1-112-2-1-1-111-2200001-2i3−i300000011i3−i3i3−i30000-12-1-10000000−i3i30000
χ3944444-2-4-4-2-2-2444-2-244-2-2-2-2-2-242-4-4-4-42-4-4-24-2-2-22222-422220000000000000000000000000000000000000000000
χ404444-24-4-44444-2-24-24-244-2-24-2-2-4-4222-4-42-2-2-2-2-2-4-422222220000000000000000000000000000000000000000000
χ414444-2-244-2-2-24-2-2-214-2-2-211-21-2-24-2-2-2-24-21-2111-2-211-211110000040000-2-200-2-2000000111100000000000000000
χ424444-2-244-2-2-24-2-2-214-2-2-211-21-2-24-2-2-2-24-21-2111-2-211-2111100000-40000220022000000-1-1-1-100000000000000000
χ434444-2-2-4-4-2-2-24-2-2-214-2-2-211-21-22-42222-421-211122-1-12-1-1-1-100000000000000000000003-3-3300000000000000000
χ444444-2-2-4-4-2-2-24-2-2-214-2-2-211-21-22-42222-421-211122-1-12-1-1-1-10000000000000000000000-333-300000000000000000
χ45444-244-4-4444-24-2-24-24-2-244-24-2-42-422-42-4-2-2-2-2-222-4-4222220000000000000000000000000000000000000000000
χ46444-24-244-2-2-2-24-21-2-2411-2-21-2-2-2-24-2-2-2-241-211111-2-2-2111100004000-2-200-2-200001111000000000000000000000
χ47444-24-244-2-2-2-24-21-2-2411-2-21-2-2-2-24-2-2-2-241-211111-2-2-211110000-40002200220000-1-1-1-1000000000000000000000
χ48444-24-2-4-4-2-2-2-24-21-2-2411-2-21-2-222-42222-41-2111-1-1222-1-1-1-10000000000000000003-3-33000000000000000000000
χ49444-24-2-4-4-2-2-2-24-21-2-2411-2-21-2-222-42222-41-2111-1-1222-1-1-1-1000000000000000000-333-3000000000000000000000
χ50444-2-2444444-2-21-2-2-2-2-2-2-2-2-2-214-2-2114-2-211111-2-2-2-211111440000-2-2000000001100000000-2-2110000000000000
χ51444-2-2444444-2-21-2-2-2-2-2-2-2-2-2-214-2-2114-2-211111-2-2-2-211111-4-400002200000000-1-10000000022-1-10000000000000
χ52444-2-24-4-4444-2-21-2-2-2-2-2-2-2-2-2-21-422-1-1-422111112222-1-1-1-1-100000000000000003-300000000003-30000000000000
χ53444-2-24-4-4444-2-21-2-2-2-2-2-2-2-2-2-21-422-1-1-422111112222-1-1-1-1-10000000000000000-330000000000-330000000000000
χ5444-444-24-422-2444-2-2-4-42222-2-24-2-4-4-4-4244-2-422-2-22-224-2-2220000000000000000000000000000000000000000000
χ5544-44-24-44-4-444-2-24-2-42-4-4224-2-2-44-2-2-24-42-2222-2-442-2222-2-20000000000000000000000000000000000000000000
χ5644-44-2-24-422-24-2-2-21-4222-1-1-21-2-2-422224-212-1-11-221-1-211-1-10000000000−2i32i30000000000i3−i3i3−i300000000000000000
χ5744-44-2-24-422-24-2-2-21-4222-1-1-21-2-2-422224-212-1-11-221-1-211-1-100000000002i3−2i30000000000−i3i3−i3i300000000000000000
χ5844-44-2-2-4422-24-2-2-21-4222-1-1-21-224-2-2-2-2-4212-1-112-2-112-1-11100000000000000−2i32i3000000i3i3−i3−i300000000000000000
χ5944-44-2-2-4422-24-2-2-21-4222-1-1-21-224-2-2-2-2-4212-1-112-2-112-1-111000000000000002i3−2i3000000−i3−i3i3i300000000000000000
χ6044-4-244-44-4-44-24-2-242-422-4-4-24-2-4-24-2-242-4-2222-22-2-44222-2-20000000000000000000000000000000000000000000
χ6144-4-24-24-422-2-24-21-22-4-1-1221-2-2-22-4222-2412-1-111-1-22-211-1-100000000−2i32i300000000i3−i3i3−i3000000000000000000000
χ6244-4-24-24-422-2-24-21-22-4-1-1221-2-2-22-4222-2412-1-111-1-22-211-1-1000000002i3−2i300000000−i3i3−i3i3000000000000000000000
χ6344-4-24-2-4422-2-24-21-22-4-1-1221-2-22-24-2-2-22-412-1-11-112-22-1-111000000000000−2i32i30000i3i3−i3−i3000000000000000000000
χ6444-4-24-2-4422-2-24-21-22-4-1-1221-2-22-24-2-2-22-412-1-11-112-22-1-1110000000000002i3−2i30000−i3−i3i3i3000000000000000000000
χ6544-4-2-244-4-4-44-2-21-2-2222222-2-21422-1-1-4-2-21-1-1-11-22-22111-1-14-40000-2-200000000110000000022-1-10000000000000
χ6644-4-2-244-4-4-44-2-21-2-2222222-2-21422-1-1-4-2-21-1-1-11-22-22111-1-1-4400002200000000-1-100000000-2-2110000000000000
χ6744-4-2-24-44-4-44-2-21-2-2222222-2-21-4-2-2114221-1-1-112-22-2-1-1-11100000000000000003-30000000000-330000000000000
χ6844-4-2-24-44-4-44-2-21-2-2222222-2-21-4-2-2114221-1-1-112-22-2-1-1-1110000000000000000-3300000000003-30000000000000
χ694-404440000-4-4-4444000000-4-4-4000000004000-40000000000022−2200000000000000000000000000022−220000000000
χ704-404440000-4-4-4444000000-4-4-4000000004000-400000000000−2222000000000000000000000000000−22220000000000
χ714-4044-200−2i32i32-4-44-2-200−2i32i3−2i32i322-400000000-20−2i32i320000000000022−22000000000000000000000000000−22i6−i600000000
χ724-4044-200−2i32i32-4-44-2-200−2i32i3−2i32i322-400000000-20−2i32i3200000000000−22220000000000000000000000000002−2−i6i600000000
χ734-4044-2002i3−2i32-4-44-2-2002i3−2i32i3−2i322-400000000-202i3−2i320000000000022−22000000000000000000000000000−22−i6i600000000
χ744-4044-2002i3−2i32-4-44-2-2002i3−2i32i3−2i322-400000000-202i3−2i3200000000000−22220000000000000000000000000002−2i6−i600000000
χ75888-4-4-488-4-4-4-4-4222-4-42222222-4-4-422-4-4-4-12-1-1-122222-1-1-1-10000000000000000000000000000000000000000000
χ76888-4-4-4-8-8-4-4-4-4-4222-4-42222222444-2-2444-12-1-1-1-2-2-2-2-211110000000000000000000000000000000000000000000
χ7788-8-4-4-48-844-4-4-422244-2-2-2-2222-444-2-24-4-4-1-211-12-22-22-1-1110000000000000000000000000000000000000000000
χ7888-8-4-4-4-8844-4-4-422244-2-2-2-22224-4-422-444-1-211-1-22-22-211-1-10000000000000000000000000000000000000000000
χ798-808-480000-8-84-48-4000000-84400000000-400040000000000000000000000000000000000000000000000000000
χ808-808-4-400−4i34i34-84-4-4200−4i34i32i3−2i34-2400000000202i3−2i3-20000000000000000000000000000000000000000000000000000
χ818-808-4-4004i3−4i34-84-4-42004i3−4i3−2i32i34-240000000020−2i32i3-20000000000000000000000000000000000000000000000000000
χ828-80-4880000-84-8-4-480000004-8400000000-400040000000000000000000000000000000000000000000000000000
χ838-80-48-400−4i34i344-8-42-4002i3−2i3−4i34i3-24400000000202i3−2i3-20000000000000000000000000000000000000000000000000000
χ848-80-48-4004i3−4i344-8-42-400−2i32i34i3−4i3-2440000000020−2i32i3-20000000000000000000000000000000000000000000000000000
χ858-80-4-480000-8442-4-400000044-20006i−6i0002000-200000006i−6i0000000000000000000000000000000000000000000
χ868-80-4-480000-8442-4-400000044-2000−6i6i0002000-20000000−6i6i0000000000000000000000000000000000000000000
χ878-80-4-4-400−4i34i3444222002i3−2i32i3−2i3-2-2-20006i−6i000-10−i3i310000033−33−3i3i0000000000000000000000000000000000000000000
χ888-80-4-4-400−4i34i3444222002i3−2i32i3−2i3-2-2-2000−6i6i000-10−i3i3100000−33333i−3i0000000000000000000000000000000000000000000
χ898-80-4-4-4004i3−4i344422200−2i32i3−2i32i3-2-2-20006i−6i000-10i3−i3100000−3333−3i3i0000000000000000000000000000000000000000000
χ908-80-4-4-4004i3−4i344422200−2i32i3−2i32i3-2-2-2000−6i6i000-10i3−i310000033−333i−3i0000000000000000000000000000000000000000000

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