Finite Group Databasebeta

← Group #13156233

Character table — Group #13156233

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11222222222224444444444444444444488888888888888181824242424242424242424242424242424242424242424242424242436363636363636363672727272216
order1223334466666333666666666121212121212121236666121212121212121212882466666666812121212121212122424242424242424248882424242461224248
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-111111111-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11-1-11111-1-1-1-11
χ41111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1
χ511111111111111111111111111111111111111111111111-1-11-1111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-111-1-1-1
χ611111111111111111111111111111111111111111111111-1-11-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111
χ711111111111111111111111111111111111111111111111-1-1-11-1-1-1-1-1-1-1-111111111111111111-1-1-111-1-1-1-1-1-111-1
χ811111111111111111111111111111111111111111111111-1-1-11-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-11
χ9222222-2-222222222222222222-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-2000000000000000000000000000000002i−2i0000002i−2i0
χ10222222-2-222222222222222222-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-200000000000000000000000000000000−2i2i000000−2i2i0
χ1122222-1222222-12-1-12-122-1-1-1-122-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1002022-1-1-1-1-1-120000000022-1-1-1-1-1-1220000000-1-1000
χ1222222-1222222-12-1-12-122-1-1-1-122-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1002022-1-1-1-1-1-1-200000000-2-2111111-2-2000000011000
χ1322222-1222222-12-1-12-122-1-1-1-122-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-20-2-211111120000000022-1-1-1-1-1-1-2-2000000011000
χ1422222-1222222-12-1-12-122-1-1-1-122-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-20-2-2111111-200000000-2-2111111220000000-1-1000
χ152222-1222-1-12-12-12-122-1-1-1-12-1-1-1222222-1-12-1-1-12-1-1-1-1-1-1-1-12222-1-122-1-1-1-1022-1-1-1-1-1-10000000000200-1-1-1-100000
χ162222-1222-1-12-12-12-122-1-1-1-12-1-1-1222222-1-12-1-1-12-1-1-1-1-1-1-1-122-2-211-2-211110-2-21111110000000000200-1-1-1-100000
χ172222-1222-1-12-12-12-122-1-1-1-12-1-1-1222222-1-12-1-1-12-1-1-1-1-1-1-1-1-2-22-2-1-122-1-1-1-10-2-21111110000000000-200111100000
χ182222-1222-1-12-12-12-122-1-1-1-12-1-1-1222222-1-12-1-1-12-1-1-1-1-1-1-1-1-2-2-2211-2-21111022-1-1-1-1-1-10000000000-200111100000
χ19222-1222222-122-1-12-12-1-122-12-122-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-10002000000002-1-122-1-1-1-1-1-122-1-1-1-100022000000-1-10
χ20222-1222222-122-1-12-12-1-122-12-122-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1000200000000-2-1-122-1-1-1-111-2-21111000-2-2000000110
χ21222-1222222-122-1-12-12-1-122-12-122-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1000-200000000211-2-21111-1-122-1-1-1-1000-2-2000000110
χ22222-1222222-122-1-12-12-1-122-12-122-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-1000-200000000-211-2-2111111-2-2111100022000000-1-10
χ23222-122-2-222-122-1-12-12-1-122-12-1-2-21-2111-2-1-1-1-1-11-2-21111110000000000000−i3i300−i3−i3i3i33−30033−3−30002i−2i000000−ii0
χ24222-122-2-222-122-1-12-12-1-122-12-1-2-21-2111-2-1-1-1-1-11-2-21111110000000000000−i3i300−i3−i3i3i3−3300−3−333000−2i2i000000i−i0
χ25222-122-2-222-122-1-12-12-1-122-12-1-2-21-2111-2-1-1-1-1-11-2-21111110000000000000i3−i300i3i3−i3−i33−30033−3−3000−2i2i000000i−i0
χ26222-122-2-222-122-1-12-12-1-122-12-1-2-21-2111-2-1-1-1-1-11-2-21111110000000000000i3−i300i3i3−i3−i3−3300−3−3330002i−2i000000−ii0
χ2722-22222-2-2-2222222-2-2-2-2-2-2222-22-2-2-2-2222-2-2-2222-22-222-2-22200000000000000000000000000000-20022-2-200000
χ2822-22222-2-2-2222222-2-2-2-2-2-2222-22-2-2-2-2222-2-2-2222-22-222-2-2-2-200000000000000000000000000000200-2-22200000
χ2922-2222-22-2-2222222-2-2-2-2-2-22222-22222-2-22-2-2-22-2-22-22-2-222000000000000000000000000000002-200000002-2000
χ3022-2222-22-2-2222222-2-2-2-2-2-22222-22222-2-22-2-2-22-2-22-22-2-22200000000000000000000000000000-220000000-22000
χ3122-222-1-22-2-222-12-1-1-21-2-211-1-12212-1-1-1-2-2-1111-111-1-2211-1-1000000−i3i3−i3−i3i3i300000000000−i3i3−i3i3−i3i32-20000000-11000
χ3222-222-1-22-2-222-12-1-1-21-2-211-1-12212-1-1-1-2-2-1111-111-1-2211-1-1000000−i3i3−i3−i3i3i300000000000i3−i3i3−i3i3−i3-2200000001-1000
χ3322-222-1-22-2-222-12-1-1-21-2-211-1-12212-1-1-1-2-2-1111-111-1-2211-1-1000000i3−i3i3i3−i3−i300000000000−i3i3−i3i3−i3i3-2200000001-1000
χ3422-222-1-22-2-222-12-1-1-21-2-211-1-12212-1-1-1-2-2-1111-111-1-2211-1-1000000i3−i3i3i3−i3−i300000000000i3−i3i3−i3i3−i32-20000000-11000
χ3522-22-122-2112-12-12-1-2-211112-1-112-2-2-2-22-1-1-211-12-11-11-1-1112200−i3i300−i3i3−i3i3000−i3i3−i3i3−i3i30000000000-200-1-11100000
χ3622-22-122-2112-12-12-1-2-211112-1-112-2-2-2-22-1-1-211-12-11-11-1-1112200i3−i300i3−i3i3−i3000i3−i3i3−i3i3−i30000000000-200-1-11100000
χ3722-22-122-2112-12-12-1-2-211112-1-112-2-2-2-22-1-1-211-12-11-11-1-111-2-200−i3i300−i3i3−i3i3000i3−i3i3−i3i3−i3000000000020011-1-100000
χ3822-22-122-2112-12-12-1-2-211112-1-112-2-2-2-22-1-1-211-12-11-11-1-111-2-200i3−i300i3−i3i3−i3000−i3i3−i3i3−i3i3000000000020011-1-100000
χ3944444-2-4-44444-24-2-24-244-2-2-2-24-42-4222-4-4-2-2-2-2-2222-4-422220000000000000000000000000000000000000000000
χ404444-24-4-4-2-24-24-24-244-2-2-2-24-2-22-4-4-4-4-4-42-24-2-2-2-4222222220000000000000000000000000000000000000000000
χ414444-2-244-2-24-2-2-2-214-2-2-211-21-2-2-24-2-2-24-21-2111-211-2-211110040-2-2-2-211110000000000000000000000000000000
χ424444-2-244-2-24-2-2-2-214-2-2-211-21-2-2-24-2-2-24-21-2111-211-2-2111100-402222-1-1-1-10000000000000000000000000000000
χ434444-2-2-4-4-2-24-2-2-2-214-2-2-211-21-222-4222-421-21112-1-122-1-1-1-1000000003-3-330000000000000000000000000000000
χ444444-2-2-4-4-2-24-2-2-2-214-2-2-211-21-222-4222-421-21112-1-122-1-1-1-100000000-333-30000000000000000000000000000000
χ45444-24-24444-24-2-21-2-2-2-2-2-2-21-2-24-2-2-211-24111111-2-2-2-21111000000000000400000000-2-2-2-2111100000000000000
χ46444-24-24444-24-2-21-2-2-2-2-2-2-21-2-24-2-2-211-24111111-2-2-2-21111000000000000-4000000002222-1-1-1-100000000000000
χ47444-24-2-4-444-24-2-21-2-2-2-2-2-2-21-2-2-4222-1-12-411111-12222-1-1-1-100000000000000000000023−2300−3−33300000000000000
χ48444-24-2-4-444-24-2-21-2-2-2-2-2-2-21-2-2-4222-1-12-411111-12222-1-1-1-1000000000000000000000−23230033−3−300000000000000
χ49444-2-2444-2-2-2-241-2-2-2411-2-2-2-21-24-24-2-2-2-21-2111-2-2-21111110004000000000-2-2-2-211110000000000000000000000
χ50444-2-2444-2-2-2-241-2-2-2411-2-2-2-21-24-24-2-2-2-21-2111-2-2-2111111000-40000000002222-1-1-1-10000000000000000000000
χ51444-2-24-4-4-2-2-2-241-2-2-2411-2-2-2-212-42-422221-2111222-1-1-1-1-1-10000000000000−2i32i300i3i3−i3−i30000000000000000000000
χ52444-2-24-4-4-2-2-2-241-2-2-2411-2-2-2-212-42-422221-2111222-1-1-1-1-1-100000000000002i3−2i300−i3−i3i3i30000000000000000000000
χ5344-444-24-4-4-444-24-2-2-42-4-422-2-24-4-2-422244-2222-2-2-224-4-2-2220000000000000000000000000000000000000000000
χ5444-44-24-44224-24-24-2-4-422224-2-2-2-44444-42-2-422-2-42-22-222-2-20000000000000000000000000000000000000000000
χ5544-44-2-24-4224-2-2-2-21-4222-1-1-21-22-2-42224-212-1-11-21-1-2211-1-10000−2i32i300i3−i3i3−i30000000000000000000000000000000
χ5644-44-2-24-4224-2-2-2-21-4222-1-1-21-22-2-42224-212-1-11-21-1-2211-1-100002i3−2i300−i3i3−i3i30000000000000000000000000000000
χ5744-44-2-2-44224-2-2-2-21-4222-1-1-21-2-224-2-2-2-4212-1-112-112-2-1-111000000−2i32i3i3i3−i3−i30000000000000000000000000000000
χ5844-44-2-2-44224-2-2-2-21-4222-1-1-21-2-224-2-2-2-4212-1-112-112-2-1-1110000002i3−2i3−i3−i3i3i30000000000000000000000000000000
χ5944-4-2444-4-4-4-244-2-242-422-4-4-24-2-442-422-24-2222-2-24-4-22-2-2220000000000000000000000000000000000000000000
χ6044-4-244-44-4-4-244-2-242-422-4-4-24-24-4-24-2-22-4-2222-22-442-222-2-20000000000000000000000000000000000000000000
χ6144-4-24-24-4-4-4-24-2-21-22222221-2-2-4-222-1-1-241-1-1-111-22-2211-1-100000000000000000000000003i−3i−3i3i00000000000000
χ6244-4-24-24-4-4-4-24-2-21-22222221-2-2-4-222-1-1-241-1-1-111-22-2211-1-10000000000000000000000000−3i3i3i−3i00000000000000
χ6344-4-24-2-44-4-4-24-2-21-22222221-2-242-2-2112-41-1-1-11-12-22-2-1-11100000000000000000000000−2i32i3i3−i3i3−i300000000000000
χ6444-4-24-2-44-4-4-24-2-21-22222221-2-242-2-2112-41-1-1-11-12-22-2-1-111000000000000000000000002i3−2i3−i3i3−i3i300000000000000
χ6544-4-2-244-422-2-241-2-22-4-1-122-2-21242-422-2-212-1-11-2-221-111-1-1000000000000000−2i32i3i3−i3i3−i30000000000000000000000
χ6644-4-2-244-422-2-241-2-22-4-1-122-2-21242-422-2-212-1-11-2-221-111-1-10000000000000002i3−2i3−i3i3−i3i30000000000000000000000
χ6744-4-2-24-4422-2-241-2-22-4-1-122-2-21-2-4-24-2-22212-1-1122-2-11-1-111000000000000000003-3-330000000000000000000000
χ6844-4-2-24-4422-2-241-2-22-4-1-122-2-21-2-4-24-2-22212-1-1122-2-11-1-11100000000000000000-333-30000000000000000000000
χ694-404440000-4-4-4444000000-4-4-4000000004000-4000000000−2i22i200000000000000000000000000000000−2i22i20000000
χ704-404440000-4-4-4444000000-4-4-4000000004000-40000000002i2−2i2000000000000000000000000000000002i2−2i20000000
χ714-404-2400−2i32i3-42-4-24-200−2i32i3−2i32i3-42200000000-20−2i32i32000000000−2i22i200000000000000000000000000000000i2−i26−600000
χ724-404-2400−2i32i3-42-4-24-200−2i32i3−2i32i3-42200000000-20−2i32i320000000002i2−2i200000000000000000000000000000000−i2i2−6600000
χ734-404-24002i3−2i3-42-4-24-2002i3−2i32i3−2i3-42200000000-202i3−2i32000000000−2i22i200000000000000000000000000000000i2−i2−6600000
χ744-404-24002i3−2i3-42-4-24-2002i3−2i32i3−2i3-42200000000-202i3−2i320000000002i2−2i200000000000000000000000000000000−i2i26−600000
χ75888-4-4-488-4-4-4-4-4222-4-42222222-4-4-4-422-4-4-12-1-1-122222-1-1-1-10000000000000000000000000000000000000000000
χ76888-4-4-4-8-8-4-4-4-4-4222-4-422222224444-2-244-12-1-1-1-2-2-2-2-211110000000000000000000000000000000000000000000
χ7788-8-4-4-48-844-4-4-422244-2-2-2-22224-444-2-2-4-4-1-211-122-22-2-1-1110000000000000000000000000000000000000000000
χ7888-8-4-4-4-8844-4-4-422244-2-2-2-2222-44-4-42244-1-211-1-2-22-2211-1-10000000000000000000000000000000000000000000
χ798-8088-40000-8-848-4-400000044-800000000-400040000000000000000000000000000000000000000000000000000
χ808-808-4-400−4i34i3-844-4-4200−4i34i32i3−2i34-2400000000202i3−2i3-20000000000000000000000000000000000000000000000000000
χ818-808-4-4004i3−4i3-844-4-42004i3−4i3−2i32i34-240000000020−2i32i3-20000000000000000000000000000000000000000000000000000
χ828-80-48800004-8-8-4-480000004-8400000000-400040000000000000000000000000000000000000000000000000000
χ838-80-48-400004-84-42-4000000-24400006i−6i002000-200000006i−6i0000000000000000000000000000000000000000000
χ848-80-48-400004-84-42-4000000-2440000−6i6i002000-20000000−6i6i0000000000000000000000000000000000000000000
χ858-80-4-4800−4i34i344-82-4-4002i3−2i3−4i34i344-200000000202i3−2i3-20000000000000000000000000000000000000000000000000000
χ868-80-4-48004i3−4i344-82-4-400−2i32i34i3−4i344-20000000020−2i32i3-20000000000000000000000000000000000000000000000000000
χ878-80-4-4-400−4i34i3444222002i3−2i32i3−2i3-2-2-200006i−6i00-10−i3i310000033−33−3i3i0000000000000000000000000000000000000000000
χ888-80-4-4-400−4i34i3444222002i3−2i32i3−2i3-2-2-20000−6i6i00-10−i3i3100000−33333i−3i0000000000000000000000000000000000000000000
χ898-80-4-4-4004i3−4i344422200−2i32i3−2i32i3-2-2-200006i−6i00-10i3−i3100000−3333−3i3i0000000000000000000000000000000000000000000
χ908-80-4-4-4004i3−4i344422200−2i32i3−2i32i3-2-2-20000−6i6i00-10i3−i310000033−333i−3i0000000000000000000000000000000000000000000

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