Finite Group Databasebeta

← Group #13155948

Character table — Group #13155948

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1122222222244444444444444444444488888888888888242424242424242424242424242424242424242424242424242424363636363636727272727272108108
order12233344666333666666661212121212121212121236666612121212121212124881212121212121212242424242424242424242424242424242222446666121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-11111111111111111-1-1-1-1-1-1-1-11-1-1-11-11-1-1-11-1-1-1
χ311111111111111111111111111111111111111111111111-1111111111-1-1-1-1-1-1-1-111111111-11-1-1-11-11-1-1-11-1-1
χ411111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ51111111111111111111111111111111111111111111111-111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-111-1-1-1-1
χ61111111111111111111111111111111111111111111111-11-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-11-11-1-1-1111
χ71111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11-11-1-1-11-111
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ9222222-2-222222222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2000000000000000000000000000002-200002-20000
χ10222222-2-222222222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-200000000000000000000000000000-220000-220000
χ1122222-122-1222-1-122-122-1-1222-1-122-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10220000000022-1-1-1-1-1-122-1-1-1-1-1-100220000-1-10000
χ1222222-122-1222-1-122-122-1-1222-1-122-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-102-20000000022-1-1-1-1-1-1-2-211111100-2-20000110000
χ1322222-122-1222-1-122-122-1-1222-1-122-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10-2200000000-2-211111122-1-1-1-1-1-100-2-20000110000
χ1422222-122-1222-1-122-122-1-1222-1-122-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10-2-200000000-2-2111111-2-211111100220000-1-10000
χ1522222-1-2-2-1222-1-122-122-1-12-2-211-2-21111-1-1-1-1-1-111-2-211110000000000000333−3−3−300333−3−3−3002-20000-110000
χ1622222-1-2-2-1222-1-122-122-1-12-2-211-2-21111-1-1-1-1-1-111-2-211110000000000000333−3−3−300−3−3−333300-2200001-10000
χ1722222-1-2-2-1222-1-122-122-1-12-2-211-2-21111-1-1-1-1-1-111-2-211110000000000000−3−3−333300333−3−3−300-2200001-10000
χ1822222-1-2-2-1222-1-122-122-1-12-2-211-2-21111-1-1-1-1-1-111-2-211110000000000000−3−3−333300−3−3−3333002-20000-110000
χ192222-122222-1-12-12-12-1-12-1-12-1222-122-1-1-12-1-1-1-12-1-1-1-1-1-1-120222-1-1-1-1-1-100000000-1-12-1-12-1-10200020-1000-100
χ202222-122222-1-12-12-12-1-12-1-12-1222-122-1-1-12-1-1-1-12-1-1-1-1-1-1-120-222-1-1-1-1-1-10000000011-211-2110-2000-201000100
χ212222-122222-1-12-12-12-1-12-1-12-1222-122-1-1-12-1-1-1-12-1-1-1-1-1-1-1-202-2-211111100000000-1-12-1-12-1-10-2000-201000100
χ222222-122222-1-12-12-12-1-12-1-12-1222-122-1-1-12-1-1-1-12-1-1-1-1-1-1-1-20-2-2-21111110000000011-211-2110200020-1000-100
χ23222-122222-12-1-12-122-1-1-12-1-1222-12-1-122-1-12-1-1-1-12-1-1-1-1-1-1220-1-122-1-1-1-1-1-12-1-12-1-100000000200020-1000-1000
χ24222-122222-12-1-12-122-1-1-12-1-1222-12-1-122-1-12-1-1-1-12-1-1-1-1-1-12-20-1-122-1-1-1-111-211-21100000000-2000-2010001000
χ25222-122222-12-1-12-122-1-1-12-1-1222-12-1-122-1-12-1-1-1-12-1-1-1-1-1-1-22011-2-21111-1-12-1-12-1-100000000-2000-2010001000
χ26222-122222-12-1-12-122-1-1-12-1-1222-12-1-122-1-12-1-1-1-12-1-1-1-1-1-1-2-2011-2-2111111-211-21100000000200020-1000-1000
χ2722-22222-2222222-2-2-2-2-22222-22-2-22-2-2222-2-2-2-222-22-222-2-200000000000000000000000000002000-202000-200
χ2822-22222-2222222-2-2-2-2-22222-22-2-22-2-2222-2-2-2-222-22-222-2-20000000000000000000000000000-200020-2000200
χ2922-2222-22222222-2-2-2-2-2222-22-222-222-2-22-2-2-2-22-22-22-2-2220000000000000000000000000002000-202000-2000
χ3022-2222-22222222-2-2-2-2-2222-22-222-222-2-22-2-2-2-22-22-22-2-222000000000000000000000000000-200020-20002000
χ3122-22-122-222-1-12-1-21-2112-1-1212-2-2-1-2-2-1-1-1-2111-121-11-1-11100000−i3i3−i3−i3i3i300000000−i3i30−i3i30−i3i302000-20-1000100
χ3222-22-122-222-1-12-1-21-2112-1-1212-2-2-1-2-2-1-1-1-2111-121-11-1-11100000−i3i3−i3−i3i3i300000000i3−i30i3−i30i3−i30-2000201000-100
χ3322-22-122-222-1-12-1-21-2112-1-1212-2-2-1-2-2-1-1-1-2111-121-11-1-11100000i3−i3i3i3−i3−i300000000−i3i30−i3i30−i3i30-2000201000-100
χ3422-22-122-222-1-12-1-21-2112-1-1212-2-2-1-2-2-1-1-1-2111-121-11-1-11100000i3−i3i3i3−i3−i300000000i3−i30i3−i30i3−i302000-20-1000100
χ3522-2-122-222-12-1-121-2-211-12-112-22-1-2-1-1-2-2-11-211-1121-111-1-1000−i3i300−i3i3−i3i3−i3i30−i3i30−i3i3000000002000-20-10001000
χ3622-2-122-222-12-1-121-2-211-12-112-22-1-2-1-1-2-2-11-211-1121-111-1-1000−i3i300−i3i3−i3i3i3−i30i3−i30i3−i300000000-2000201000-1000
χ3722-2-122-222-12-1-121-2-211-12-112-22-1-2-1-1-2-2-11-211-1121-111-1-1000i3−i300i3−i3i3−i3−i3i30−i3i30−i3i300000000-2000201000-1000
χ3822-2-122-222-12-1-121-2-211-12-112-22-1-2-1-1-2-2-11-211-1121-111-1-1000i3−i300i3−i3i3−i3i3−i30i3−i30i3−i3000000002000-20-10001000
χ394444-24-4-444-2-24-24-24-2-24-2-2-42-4-4-42-4-422-24-2-2-2-2-4222222200000000000000000000000000000000000000000
χ404444-2-244-24-2-2-214-2-2-2-2-21-24-2-2-24-2-2-2111-21111-21-2-211110040000000000000000-2-2-211-21100000000000000
χ414444-2-244-24-2-2-214-2-2-2-2-21-24-2-2-24-2-2-2111-21111-21-2-2111100-40000000000000000222-1-12-1-100000000000000
χ424444-2-2-4-4-24-2-2-214-2-2-2-2-21-2-4222-4222-1-11-211112-122-1-1-1-100000000000000000000023−3−3−233300000000000000
χ434444-2-2-4-4-24-2-2-214-2-2-2-2-21-2-4222-4222-1-11-211112-122-1-1-1-1000000000000000000000−233323−3−300000000000000
χ44444-244-4-44-24-2-24-244-2-2-24-22-4-4-42-422-4-4-2-24-2-2-22-422222200000000000000000000000000000000000000000
χ45444-24-244-2-24-21-2-24-2-2-21-2-2-24-2-2-2411-2-211-21111-2-2-2111104000000000-2-2-211-2110000000000000000000000
χ46444-24-244-2-24-21-2-24-2-2-21-2-2-24-2-2-2411-2-211-21111-2-2-211110-4000000000222-1-12-1-10000000000000000000000
χ47444-24-2-4-4-2-24-21-2-24-2-2-21-2-22-4222-4-1-12211-2111-1222-1-1-1-1000000000000023−3−3−23330000000000000000000000
χ48444-24-2-4-4-2-24-21-2-24-2-2-21-2-22-4222-4-1-12211-2111-1222-1-1-1-10000000000000−233323−3−30000000000000000000000
χ49444-2-24444-2-21-2-2-2-2411-2-21-2-244-2-2-2-2-2-21-2-2111-2-2111111400-2-2-2-21111000000000000000000000000000000
χ50444-2-24444-2-21-2-2-2-2411-2-21-2-244-2-2-2-2-2-21-2-2111-2-2111111-4002222-1-1-1-1000000000000000000000000000000
χ51444-2-24-4-44-2-21-2-2-2-2411-2-2122-4-42222221-2-211122-1-1-1-1-1-100000003-3-33000000000000000000000000000000
χ52444-2-24-4-44-2-21-2-2-2-2411-2-2122-4-42222221-2-211122-1-1-1-1-1-10000000-333-3000000000000000000000000000000
χ5344-444-24-4-2444-2-2-4-42-4-4-2-244-4-22-4422-2-2-22222-2-224-4-2-22200000000000000000000000000000000000000000
χ5444-444-2-44-2444-2-2-4-42-4-4-2-24-442-24-4-2-222-22222-22-2-4422-2-200000000000000000000000000000000000000000
χ5544-44-24-4444-2-24-2-42-4224-2-2-4-2-44424422-2-4222-2-4-22-222-2-200000000000000000000000000000000000000000
χ5644-44-2-24-4-24-2-2-21-42222-21-242-22-4-2221112-1-1-11-2-1-2211-1-10000000000000000000−2i32i30i3−i30i3−i300000000000000
χ5744-44-2-24-4-24-2-2-21-42222-21-242-22-4-2221112-1-1-11-2-1-2211-1-100000000000000000002i3−2i30−i3i30−i3i300000000000000
χ5844-44-2-2-44-24-2-2-21-42222-21-2-4-22-242-2-2-1-112-1-1-11212-2-1-11100000000000000000000003i−3i0−3i3i00000000000000
χ5944-44-2-2-44-24-2-2-21-42222-21-2-4-22-242-2-2-1-112-1-1-11212-2-1-1110000000000000000000000−3i3i03i−3i00000000000000
χ6044-4-2444-44-24-2-242-4-422-24-2-2-44-4242244-22-422-2-2-4-22-2-22200000000000000000000000000000000000000000
χ6144-4-24-24-4-2-24-21-22-42221-2-2-2-4-2224-1-1-2-21-12-1-1112-2211-1-1000000000000003i−3i0−3i3i0000000000000000000000
χ6244-4-24-24-4-2-24-21-22-42221-2-2-2-4-2224-1-1-2-21-12-1-1112-2211-1-100000000000000−3i3i03i−3i0000000000000000000000
χ6344-4-24-2-44-2-24-21-22-42221-2-2242-2-2-411221-12-1-11-1-22-2-1-11100000000000−2i32i30i3−i30i3−i30000000000000000000000
χ6444-4-24-2-44-2-24-21-22-42221-2-2242-2-2-411221-12-1-11-1-22-2-1-111000000000002i3−2i30−i3i30−i3i30000000000000000000000
χ6544-4-2-244-44-2-21-2-222-4-1-1-2-21-224-42-222-2-2122-1-11-221-111-1-100000−2i32i3i3i3−i3−i3000000000000000000000000000000
χ6644-4-2-244-44-2-21-2-222-4-1-1-2-21-224-42-222-2-2122-1-11-221-111-1-1000002i3−2i3−i3−i3i3i3000000000000000000000000000000
χ6744-4-2-24-444-2-21-2-222-4-1-1-2-212-2-44-22-2-222122-1-112-2-11-1-111000−2i32i300i3−i3i3−i3000000000000000000000000000000
χ6844-4-2-24-444-2-21-2-222-4-1-1-2-212-2-44-22-2-222122-1-112-2-11-1-1110002i3−2i300−i3i3−i3i3000000000000000000000000000000
χ694-4044400-4-4-444400000-4-4-4000000000040000-4000000000000000000000000000000000000000000000002i−2i
χ704-4044400-4-4-444400000-4-4-4000000000040000-400000000000000000000000000000000000000000000000−2i2i
χ71888-4-4-488-4-4-4222-4-4-422222-4-4-4-4-4-42222-122-1-1-12222-1-1-1-100000000000000000000000000000000000000000
χ72888-4-4-4-8-8-4-4-4222-4-4-422222444444-2-2-2-2-122-1-1-1-2-2-2-2111100000000000000000000000000000000000000000
χ7388-8-4-4-48-8-4-4-4222444-2-2222-44-444-4-2-222-1-2-211-12-22-2-1-11100000000000000000000000000000000000000000
χ7488-8-4-4-4-88-4-4-4222444-2-22224-44-4-4422-2-2-1-2-211-1-22-2211-1-100000000000000000000000000000000000000000
χ758-8088-4004-8-88-4-40000044-80000000000-4000040000000000000000000000000000000000000000000000000
χ768-808-4800-8-84-48-400000-8440000000000-4000040000000000000000000000000000000000000000000000000
χ778-808-4-4004-84-4-42000004-24000000006i−6i20000-200006i−6i0000000000000000000000000000000000000000000
χ788-808-4-4004-84-4-42000004-2400000000−6i6i20000-20000−6i6i0000000000000000000000000000000000000000000
χ798-80-48800-84-8-4-48000004-840000000000-4000040000000000000000000000000000000000000000000000000
χ808-80-48-40044-8-42-400000-2440000006i−6i0020000-20000006i−6i00000000000000000000000000000000000000000
χ818-80-48-40044-8-42-400000-244000000−6i6i0020000-2000000−6i6i00000000000000000000000000000000000000000
χ828-80-4-4800-8442-4-40006-644-200000000002006-6-20000000000000000000000000000000000000000000000000
χ838-80-4-4800-8442-4-4000-6644-20000000000200-66-20000000000000000000000000000000000000000000000000
χ848-80-4-4-4004442220006-6-2-2-20000006i−6i6i−6i-100-3310000−3i3i−3i3i00000000000000000000000000000000000000000
χ858-80-4-4-4004442220006-6-2-2-2000000−6i6i−6i6i-100-33100003i−3i3i−3i00000000000000000000000000000000000000000
χ868-80-4-4-400444222000-66-2-2-20000006i−6i−6i6i-1003-3100003i−3i−3i3i00000000000000000000000000000000000000000
χ878-80-4-4-400444222000-66-2-2-2000000−6i6i6i−6i-1003-310000−3i3i3i−3i00000000000000000000000000000000000000000

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