Finite Group Databasebeta

← Group #13156261

Character table — Group #13156261

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size112222222222244444444444444444444888888888888881212181824242424242424242424242424242424242424242424242424243636363636727272727272108108
order1223334466666333666666666121212121212121236666121212121212121212888844121212121212121212121212121212122424242424242424824242424882424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-111
χ31111111111111111111111111111111111111111111111111-1-11-111-1-111-1-11111-1-1-1-111111111-1-1-1-1-11-111-1-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-11-1-111-1-111-1-1-1-1111111111111-1-1-1-1-1-11-1-111-1-1
χ511111111111111111111111111111111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
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
χ711111111111111111111111111111111111111111111111-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111
χ811111111111111111111111111111111111111111111111-1-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111
χ9222222-2-222222222222222222-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-22i−2i000000000000000000002i2i2i2i−2i−2i−2i−2i0000000000000
χ10222222-2-222222222222222222-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-2−2i2i00000000000000000000−2i−2i−2i−2i2i2i2i2i0000000000000
χ1122222-122222-122-1-12-122-1-1-12-122-1-1-12-12-1-1-1-1-1-122-1-1-1-1-1-122000200-1-100220000-1-1-1-12-1-1-12-1-1-1000000200-1-100
χ1222222-122222-122-1-12-122-1-1-12-122-1-1-12-12-1-1-1-1-1-122-1-1-1-1-1-122000-2001100-2-2000011112-1-1-12-1-1-1000000-2001100
χ1322222-122222-122-1-12-122-1-1-12-122-1-1-12-12-1-1-1-1-1-122-1-1-1-1-1-1-2-2000200-1-100220000-1-1-1-1-2111-2111000000-2001100
χ1422222-122222-122-1-12-122-1-1-12-122-1-1-12-12-1-1-1-1-1-122-1-1-1-1-1-1-2-2000-2001100-2-200001111-2111-2111000000200-1-100
χ1522222-1-2-2222-122-1-12-122-1-1-12-1-2-2111-21-2-1-1-1-1-11-2-21111112i−2i000000−i3i300000000−i3−i3i3i32i−i−i−i−2iiii0000000003−300
χ1622222-1-2-2222-122-1-12-122-1-1-12-1-2-2111-21-2-1-1-1-1-11-2-21111112i−2i000000i3−i300000000i3i3−i3−i32i−i−i−i−2iiii000000000−3300
χ1722222-1-2-2222-122-1-12-122-1-1-12-1-2-2111-21-2-1-1-1-1-11-2-2111111−2i2i000000−i3i300000000−i3−i3i3i3−2iiii2i−i−i−i000000000−3300
χ1822222-1-2-2222-122-1-12-122-1-1-12-1-2-2111-21-2-1-1-1-1-11-2-2111111−2i2i000000i3−i300000000i3i3−i3−i3−2iiii2i−i−i−i0000000003−300
χ192222-122222-122-12-1-12-1-122-1-122-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1220020-1-1002200-1-1-1-10000-12-1-1-12-1-10000020-1-10000
χ202222-122222-122-12-1-12-1-122-1-122-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12200-201100-2-20011110000-12-1-1-12-1-100000-20110000
χ212222-122222-122-12-1-12-1-122-1-122-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-20020-1-1002200-1-1-1-100001-2111-21100000-20110000
χ222222-122222-122-12-1-12-1-122-1-122-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-200-201100-2-200111100001-2111-2110000020-1-10000
χ232222-12-2-222-122-12-1-12-1-122-1-12-21-2111-2-2-1-1-1-1-1111-2-211112i−2i0000−i3i3000000−i3−i3i3i30000−i2i−i−ii−2iii00000003−30000
χ242222-12-2-222-122-12-1-12-1-122-1-12-21-2111-2-2-1-1-1-1-1111-2-211112i−2i0000i3−i3000000i3i3−i3−i30000−i2i−i−ii−2iii0000000−330000
χ252222-12-2-222-122-12-1-12-1-122-1-12-21-2111-2-2-1-1-1-1-1111-2-21111−2i2i0000−i3i3000000−i3−i3i3i30000i−2iii−i2i−i−i0000000−330000
χ262222-12-2-222-122-12-1-12-1-122-1-12-21-2111-2-2-1-1-1-1-1111-2-21111−2i2i0000i3−i3000000i3i3−i3−i30000i−2iii−i2i−i−i00000003−30000
χ27222-12222-1-122-1-1-1222-1-1-1-12-1-1-1222222-1-12-1-1-12-1-1-1-1-1-1-1-10022222222-1-1-1-1-1-1-1-1-1-1-1-1000000002-1-1-1-100000000
χ28222-12222-1-122-1-1-1222-1-1-1-12-1-1-1222222-1-12-1-1-12-1-1-1-1-1-1-1-10022-2-2-2-2-2-2111111111111000000002-1-1-1-100000000
χ29222-12222-1-122-1-1-1222-1-1-1-12-1-1-1222222-1-12-1-1-12-1-1-1-1-1-1-1-100-2-22-222-2-2-1-111-1-1-1-1111100000000-2111100000000
χ30222-12222-1-122-1-1-1222-1-1-1-12-1-1-1222222-1-12-1-1-12-1-1-1-1-1-1-1-100-2-2-22-2-22211-1-11111-1-1-1-100000000-2111100000000
χ3122-22222-2-2-2222222-2-2-2-2-2-2222-22222-2-222-2-2-22-22-22-222-2-2002200000000000000000000000000-222-2-200000000
χ3222-22222-2-2-2222222-2-2-2-2-2-2222-22222-2-222-2-2-22-22-22-222-2-200-2-2000000000000000000000000002-2-22200000000
χ3322-2222-22-2-2222222-2-2-2-2-2-22222-2-2-2-222-22-2-2-222-22-22-2-222000000000000000000000000000000000000000002-2
χ3422-2222-22-2-2222222-2-2-2-2-2-22222-2-2-2-222-22-2-2-222-22-22-2-22200000000000000000000000000000000000000000-22
χ3522-2-1222-21122-1-1-12-2-211112-1-112222-2-2-1-1-211-1-2-11-11-1-1110022000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300000000-2-1-11100000000
χ3622-2-1222-21122-1-1-12-2-211112-1-112222-2-2-1-1-211-1-2-11-11-1-1110022000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300000000-2-1-11100000000
χ3722-2-1222-21122-1-1-12-2-211112-1-112222-2-2-1-1-211-1-2-11-11-1-11100-2-2000000−i3i3i3−i3−i3i3−i3i3i3−i3i3−i300000000211-1-100000000
χ3822-2-1222-21122-1-1-12-2-211112-1-112222-2-2-1-1-211-1-2-11-11-1-11100-2-2000000i3−i3−i3i3i3−i3i3−i3−i3i3−i3i300000000211-1-100000000
χ394444-2-24444-2-24-2-21-2-2-2-2-2-21-2-24-2-211-2-24111111-2-2-2-211114400000000000000000000-2-211-2-2110000000000000
χ404444-2-24444-2-24-2-21-2-2-2-2-2-21-2-24-2-211-2-24111111-2-2-2-21111-4-40000000000000000000022-1-122-1-10000000000000
χ414444-2-2-4-444-2-24-2-21-2-2-2-2-2-21-2-2-422-1-122-411111-12222-1-1-1-14i−4i00000000000000000000−2i−2iii2i2i−i−i0000000000000
χ424444-2-2-4-444-2-24-2-21-2-2-2-2-2-21-2-2-422-1-122-411111-12222-1-1-1-1−4i4i000000000000000000002i2i−i−i−2i−2iii0000000000000
χ43444-244-4-4-2-244-2-2-2444-2-2-2-24-2-22-4-4-4-4-4-42-24-2-2-2-4222222220000000000000000000000000000000000000000000
χ44444-24-244-2-24-2-2-21-24-2-2-211-2-21-24-2-2-24-2-21-2111-2-2-211111100000400-2-200-2-200001111000000000000000000000
χ45444-24-244-2-24-2-2-21-24-2-2-211-2-21-24-2-2-24-2-21-2111-2-2-211111100000-4002200220000-1-1-1-1000000000000000000000
χ46444-24-2-4-4-2-24-2-2-21-24-2-2-211-2-212-4222-4221-2111222-1-1-1-1-1-100000000−2i32i300000000i3i3−i3−i3000000000000000000000
χ47444-24-2-4-4-2-24-2-2-21-24-2-2-211-2-212-4222-4221-2111222-1-1-1-1-1-1000000002i3−2i300000000−i3−i3i3i3000000000000000000000
χ48444-2-2444-2-2-24-21-2-2-2411-2-2-21-2-2-24-2-2-24-21-2111-211-2-21111000040-2-200-2-20011110000000000000000000000000
χ49444-2-2444-2-2-24-21-2-2-2411-2-2-21-2-2-24-2-2-24-21-2111-211-2-211110000-4022002200-1-1-1-10000000000000000000000000
χ50444-2-24-4-4-2-2-24-21-2-2-2411-2-2-21-222-4222-421-21112-1-122-1-1-1-1000000−2i32i3000000i3i3−i3−i30000000000000000000000000
χ51444-2-24-4-4-2-2-24-21-2-2-2411-2-2-21-222-4222-421-21112-1-122-1-1-1-10000002i3−2i3000000−i3−i3i3i30000000000000000000000000
χ5244-444-24-4-4-44-244-2-2-42-4-422-24-2-44-2-2-2-424-2222-224-4-22-2-2220000000000000000000000000000000000000000000
χ5344-444-2-44-4-44-244-2-2-42-4-422-24-24-42224-2-4-2222-2-2-442-222-2-20000000000000000000000000000000000000000000
χ5444-44-244-4-4-4-244-24-22-422-4-4-2-24-4-24-2-22-44-2222-22-224-4-2-2220000000000000000000000000000000000000000000
χ5544-44-24-44-4-4-244-24-22-422-4-4-2-2442-422-24-4-2222-2-22-2-4422-2-20000000000000000000000000000000000000000000
χ5644-44-2-24-4-4-4-2-24-2-212222221-2-2-4-2-2112241-1-1-11-1-22-2211-1-10000000000000000000000003-3003-30000000000000
χ5744-44-2-24-4-4-4-2-24-2-212222221-2-2-4-2-2112241-1-1-11-1-22-2211-1-1000000000000000000000000-3300-330000000000000
χ5844-44-2-2-44-4-4-2-24-2-212222221-2-2422-1-1-2-2-41-1-1-1112-22-2-1-1110000000000000000000000003i−3i00−3i3i0000000000000
χ5944-44-2-2-44-4-4-2-24-2-212222221-2-2422-1-1-2-2-41-1-1-1112-22-2-1-111000000000000000000000000−3i3i003i−3i0000000000000
χ6044-4-244-442244-2-2-24-4-422224-2-2-2-4-4-4-4442-2-422-242-22-222-2-20000000000000000000000000000000000000000000
χ6144-4-24-24-4224-2-2-21-2-4222-1-1-2-2124-2-2-2-42-212-1-112-221-111-1-1000000000000−2i32i30000i3−i3i3−i3000000000000000000000
χ6244-4-24-24-4224-2-2-21-2-4222-1-1-2-2124-2-2-2-42-212-1-112-221-111-1-10000000000002i3−2i30000−i3i3−i3i3000000000000000000000
χ6344-4-24-2-44224-2-2-21-2-4222-1-1-2-21-2-42224-2212-1-11-22-2-11-1-1110000000000000000003-3-33000000000000000000000
χ6444-4-24-2-44224-2-2-21-2-4222-1-1-2-21-2-42224-2212-1-11-22-2-11-1-111000000000000000000-333-3000000000000000000000
χ6544-4-2-244-422-24-21-2-22-4-1-122-21-22-24-2-22-4-212-1-1121-1-2211-1-10000000000−2i32i300i3−i3i3−i30000000000000000000000000
χ6644-4-2-244-422-24-21-2-22-4-1-122-21-22-24-2-22-4-212-1-1121-1-2211-1-100000000002i3−2i300−i3i3−i3i30000000000000000000000000
χ6744-4-2-24-4422-24-21-2-22-4-1-122-21-2-22-422-24212-1-11-2-112-2-1-111000000000000003-3-330000000000000000000000000
χ6844-4-2-24-4422-24-21-2-22-4-1-122-21-2-22-422-24212-1-11-2-112-2-1-11100000000000000-333-30000000000000000000000000
χ694-404440000-4-4-4444000000-4-4-4000000004000-40000000000022−2200000000000000000000000000022−220000000000
χ704-404440000-4-4-4444000000-4-4-4000000004000-400000000000−2222000000000000000000000000000−22220000000000
χ714-40-24400−2i32i3-4-42-2-2400−2i32i3−2i32i3-42200000000-20−2i32i320000000000022−22000000000000000000000000000−22i6−i600000000
χ724-40-24400−2i32i3-4-42-2-2400−2i32i3−2i32i3-42200000000-20−2i32i3200000000000−22220000000000000000000000000002−2−i6i600000000
χ734-40-244002i3−2i3-4-42-2-24002i3−2i32i3−2i3-42200000000-202i3−2i320000000000022−22000000000000000000000000000−22−i6i600000000
χ744-40-244002i3−2i3-4-42-2-24002i3−2i32i3−2i3-42200000000-202i3−2i3200000000000−22220000000000000000000000000002−2i6−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
χ7788-8-4-4-48-844-4-4-422244-2-2-2-22224-4-42244-4-1-211-1-22-22-2-1-1110000000000000000000000000000000000000000000
χ7888-8-4-4-4-8844-4-4-422244-2-2-2-2222-444-2-2-4-44-1-211-12-22-2211-1-10000000000000000000000000000000000000000000
χ798-8088-40000-84-88-4-40000004-8400000000-400040000000000000000000000000000000000000000000000000000
χ808-808-4800004-8-8-48-400000044-800000000-400040000000000000000000000000000000000000000000000000000
χ818-808-4-4000044-8-4-42000000-2440006i−6i0002000-2000006i−6i000000000000000000000000000000000000000000000
χ828-808-4-4000044-8-4-42000000-244000−6i6i0002000-200000−6i6i000000000000000000000000000000000000000000000
χ838-80-48-400−4i34i3-844-42-400−4i34i32i3−2i344-200000000202i3−2i3-20000000000000000000000000000000000000000000000000000
χ848-80-48-4004i3−4i3-844-42-4004i3−4i3−2i32i344-20000000020−2i32i3-20000000000000000000000000000000000000000000000000000
χ858-80-4-4800−4i34i34-842-4-4002i3−2i3−4i34i34-2400000000202i3−2i3-20000000000000000000000000000000000000000000000000000
χ868-80-4-48004i3−4i34-842-4-400−2i32i34i3−4i34-240000000020−2i32i3-20000000000000000000000000000000000000000000000000000
χ878-80-4-4-400−4i34i3444222002i3−2i32i3−2i3-2-2-20006i−6i000-10−i3i3100000−3i3i33−330000000000000000000000000000000000000000000
χ888-80-4-4-400−4i34i3444222002i3−2i32i3−2i3-2-2-2000−6i6i000-10−i3i31000003i−3i−33330000000000000000000000000000000000000000000
χ898-80-4-4-4004i3−4i344422200−2i32i3−2i32i3-2-2-20006i−6i000-10i3−i3100000−3i3i−33330000000000000000000000000000000000000000000
χ908-80-4-4-4004i3−4i344422200−2i32i3−2i32i3-2-2-2000−6i6i000-10i3−i31000003i−3i33−330000000000000000000000000000000000000000000

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