Finite Group Databasebeta

← Group #13155931

Character table — Group #13155931

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1122222222244444444444444444444488888888888888242424242424242424242424242424242424242424242424242424363636363636727272727272108108
order12233344666333666666661212121212121212121236666612121212121212122666666668824242424242424242424242424242424224444661212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-111111111-1-1-1-1-1-1-1-11-11-1-1-11-11-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111-11-1-1-1-1-1-1-1-111111111-11-11-1-1-11-11-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1-11-11-1-1-11-11-1-111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-11-1-1-11-11-1-1-111
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
χ9222222-2-222222222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-200000000000000000000000000000002-200002-200
χ10222222-2-222222222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-20000000000000000000000000000000-220000-2200
χ1122222-1222-122-1-122-1-1-12-1-12-12-12222-1-1-12-1-1-1-12-1-1-1-1-1-1-1222-1-1-1-1-1-1020000000022-1-1-1-1-1-10202000-10-10000
χ1222222-1222-122-1-122-1-1-12-1-12-12-12222-1-1-12-1-1-1-12-1-1-1-1-1-1-1222-1-1-1-1-1-10-200000000-2-21111110-20-20001010000
χ1322222-1222-122-1-122-1-1-12-1-12-12-12222-1-1-12-1-1-1-12-1-1-1-1-1-1-1-2-2-2111111020000000022-1-1-1-1-1-10-20-20001010000
χ1422222-1222-122-1-122-1-1-12-1-12-12-12222-1-1-12-1-1-1-12-1-1-1-1-1-1-1-2-2-21111110-200000000-2-21111110202000-10-10000
χ152222-1222-122-12-12-12-1-1-12-1-12-1222-1-122-1-12-1-1-1-12-1-1-1-1-1-12-1-122-1-1-1-12022-1-1-1-1-1-100000000202000-10-100000
χ162222-1222-122-12-12-12-1-1-12-1-12-1222-1-122-1-12-1-1-1-12-1-1-1-1-1-12-1-122-1-1-1-1-20-2-211111100000000-20-200010100000
χ172222-1222-122-12-12-12-1-1-12-1-12-1222-1-122-1-12-1-1-1-12-1-1-1-1-1-1-211-2-211112022-1-1-1-1-1-100000000-20-200010100000
χ182222-1222-122-12-12-12-1-1-12-1-12-1222-1-122-1-12-1-1-1-12-1-1-1-1-1-1-211-2-21111-20-2-211111100000000202000-10-100000
χ19222-1222222-1-1-12-12222-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100000000022-1-122-1-1-1-1-1-122-1-1-1-10000220000-1-100
χ20222-1222222-1-1-12-12222-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000000002-2-1-122-1-1-1-111-2-211110000-2-200001100
χ21222-1222222-1-1-12-12222-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000-2211-2-21111-1-122-1-1-1-10000-2-200001100
χ22222-1222222-1-1-12-12222-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000-2-211-2-2111111-2-211110000220000-1-100
χ23222-122-2-222-1-1-12-12222-1-12-2-2-2-2111111-1-1-1-1-1-111-2-21111000000000003−30033−3−33−30033−3−300002-20000-1100
χ24222-122-2-222-1-1-12-12222-1-12-2-2-2-2111111-1-1-1-1-1-111-2-21111000000000003−30033−3−3−3300−3−3330000-2200001-100
χ25222-122-2-222-1-1-12-12222-1-12-2-2-2-2111111-1-1-1-1-1-111-2-2111100000000000−3300−3−3333−30033−3−30000-2200001-100
χ26222-122-2-222-1-1-12-12222-1-12-2-2-2-2111111-1-1-1-1-1-111-2-2111100000000000−3300−3−333−3300−3−33300002-20000-1100
χ2722-22222-2222222-2-2-2-2-22222-2-222-2-2-2222-2-2-2-222-22-222-2-2000000000000000000000000000020-200020-20000
χ2822-22222-2222222-2-2-2-2-22222-2-222-2-2-2222-2-2-2-222-22-222-2-20000000000000000000000000000-202000-2020000
χ2922-2222-22222222-2-2-2-2-2222-222-2-2222-2-22-2-2-2-22-22-22-2-22200000000000000000000000000020-200020-200000
χ3022-2222-22222222-2-2-2-2-2222-222-2-2222-2-22-2-2-2-22-22-22-2-222000000000000000000000000000-202000-20200000
χ3122-222-12-22-122-1-1-2-21112-1-121-2-12-2-2-2-1-1-1-2111-121-11-1-111000−i3i3−i3−i3i3i3000000000000−i3i3−i3i3−i3i3020-2000-1010000
χ3222-222-12-22-122-1-1-2-21112-1-121-2-12-2-2-2-1-1-1-2111-121-11-1-111000−i3i3−i3−i3i3i3000000000000i3−i3i3−i3i3−i30-20200010-10000
χ3322-222-12-22-122-1-1-2-21112-1-121-2-12-2-2-2-1-1-1-2111-121-11-1-111000i3−i3i3i3−i3−i3000000000000−i3i3−i3i3−i3i30-20200010-10000
χ3422-222-12-22-122-1-1-2-21112-1-121-2-12-2-2-2-1-1-1-2111-121-11-1-111000i3−i3i3i3−i3−i3000000000000i3−i3i3−i3i3−i3020-2000-1010000
χ3522-22-12-22-122-12-1-21-211-12-112-1-2-22-1-1-2-2-11-211-1121-111-1-10−i3i300−i3i3−i3i30000−i3i3−i3i3−i3i30000000020-2000-10100000
χ3622-22-12-22-122-12-1-21-211-12-112-1-2-22-1-1-2-2-11-211-1121-111-1-10−i3i300−i3i3−i3i30000i3−i3i3−i3i3−i300000000-20200010-100000
χ3722-22-12-22-122-12-1-21-211-12-112-1-2-22-1-1-2-2-11-211-1121-111-1-10i3−i300i3−i3i3−i30000−i3i3−i3i3−i3i300000000-20200010-100000
χ3822-22-12-22-122-12-1-21-211-12-112-1-2-22-1-1-2-2-11-211-1121-111-1-10i3−i300i3−i3i3−i30000i3−i3i3−i3i3−i30000000020-2000-10100000
χ3944444-2-4-44-244-2-244-2-2-24-2-2-42-42-4-4-4-422-24-2-2-2-2-4222222200000000000000000000000000000000000000000
χ404444-24-4-4-244-24-24-24-2-2-24-22-42-4-4-422-4-4-2-24-2-2-22-422222200000000000000000000000000000000000000000
χ414444-2-244-2-24-2-214-2-211-2-21-2-2-2-244-2-2-2-21-2-2111-2-21111114-2-2-2-2111100000000000000000000000000000000
χ424444-2-244-2-24-2-214-2-211-2-21-2-2-2-244-2-2-2-21-2-2111-2-2111111-42222-1-1-1-100000000000000000000000000000000
χ434444-2-2-4-4-2-24-2-214-2-211-2-212222-4-422221-2-211122-1-1-1-1-1-1000003-3-3300000000000000000000000000000000
χ444444-2-2-4-4-2-24-2-214-2-211-2-212222-4-422221-2-211122-1-1-1-1-1-100000-333-300000000000000000000000000000000
χ45444-24-2444-2-2-21-2-24-2-2-2-21-24-24-2-2-2-2-2111-21111-21-2-211110000000000400000000-2-2-2-2111100000000000000
χ46444-24-2444-2-2-21-2-24-2-2-2-21-24-24-2-2-2-2-2111-21111-21-2-211110000000000-4000000002222-1-1-1-100000000000000
χ47444-24-2-4-44-2-2-21-2-24-2-2-2-21-2-42-422222-1-11-211112-122-1-1-1-1000000000000000000023−2300−3−33300000000000000
χ48444-24-2-4-44-2-2-21-2-24-2-2-2-21-2-42-422222-1-11-211112-122-1-1-1-10000000000000000000−23230033−3−300000000000000
χ49444-2-2444-24-21-2-2-2-24-2-21-2-2-24-24-2-211-2-211-21111-2-2-2111100000000040-2-2-2-211110000000000000000000000
χ50444-2-2444-24-21-2-2-2-24-2-21-2-2-24-24-2-211-2-211-21111-2-2-21111000000000-402222-1-1-1-10000000000000000000000
χ51444-2-24-4-4-24-21-2-2-2-24-2-21-2-22-42-422-1-12211-2111-1222-1-1-1-10000000000023−2300−3−3330000000000000000000000
χ52444-2-24-4-4-24-21-2-2-2-24-2-21-2-22-42-422-1-12211-2111-1222-1-1-1-100000000000−23230033−3−30000000000000000000000
χ5344-444-2-444-244-2-2-4-42224-2-2-4-242-444422-2-4222-2-4-22-222-2-200000000000000000000000000000000000000000
χ5444-44-244-4-244-24-2-42-422-24-2-2-4244-42244-22-422-2-2-4-22-2-22200000000000000000000000000000000000000000
χ5544-44-2-24-4-2-24-2-21-422-1-1-2-21-222-24-422-2-2122-1-11-221-111-1-1000−2i32i3i3i3−i3−i300000000000000000000000000000000
χ5644-44-2-24-4-2-24-2-21-422-1-1-2-21-222-24-422-2-2122-1-11-221-111-1-10002i3−2i3−i3−i3i3i300000000000000000000000000000000
χ5744-44-2-2-44-2-24-2-21-422-1-1-2-212-2-22-44-2-222122-1-112-2-11-1-1110−2i32i300i3−i3i3−i300000000000000000000000000000000
χ5844-44-2-2-44-2-24-2-21-422-1-1-2-212-2-22-44-2-222122-1-112-2-11-1-11102i3−2i300−i3i3−i3i300000000000000000000000000000000
χ5944-4-2444-444-2-2-242-4-4-4-4-2-244-4-44-2222-2-2-22222-2-224-4-2-22200000000000000000000000000000000000000000
χ6044-4-244-4444-2-2-242-4-4-4-4-2-24-444-42-2-2-222-22222-22-2-4422-2-200000000000000000000000000000000000000000
χ6144-4-24-24-44-2-2-21-22-4222-21-242-4-2-22221112-1-1-11-2-1-2211-1-1000000000000000000000−2i32i3i3−i3i3−i300000000000000
χ6244-4-24-24-44-2-2-21-22-4222-21-242-4-2-22221112-1-1-11-2-1-2211-1-10000000000000000000002i3−2i3−i3i3−i3i300000000000000
χ6344-4-24-2-444-2-2-21-22-4222-21-2-4-2422-2-2-2-1-112-1-1-11212-2-1-111000000000000000000000003i−3i−3i3i00000000000000
χ6444-4-24-2-444-2-2-21-22-4222-21-2-4-2422-2-2-2-1-112-1-1-11212-2-1-11100000000000000000000000−3i3i3i−3i00000000000000
χ6544-4-2-244-4-24-21-2-222-4221-2-2-2-424-22-1-1-2-21-12-1-1112-2211-1-10000000000000003i−3i−3i3i0000000000000000000000
χ6644-4-2-244-4-24-21-2-222-4221-2-2-2-424-22-1-1-2-21-12-1-1112-2211-1-1000000000000000−3i3i3i−3i0000000000000000000000
χ6744-4-2-24-44-24-21-2-222-4221-2-224-2-42-211221-12-1-11-1-22-2-1-1110000000000000−2i32i3i3−i3i3−i30000000000000000000000
χ6844-4-2-24-44-24-21-2-222-4221-2-224-2-42-211221-12-1-11-1-22-2-1-11100000000000002i3−2i3−i3i3−i3i30000000000000000000000
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
χ7388-8-4-4-48-8-4-4-4222444-2-2222-444-4-44-2-222-1-2-211-12-22-2-1-11100000000000000000000000000000000000000000
χ7488-8-4-4-4-88-4-4-4222444-2-22224-4-444-422-2-2-1-2-211-1-22-2211-1-100000000000000000000000000000000000000000
χ758-8088-400-84-88-4-400000-8440000000000-4000040000000000000000000000000000000000000000000000000
χ768-808-48004-8-8-48-4000004-840000000000-4000040000000000000000000000000000000000000000000000000
χ778-808-4-40044-8-4-420006-644-200000000002006-6-20000000000000000000000000000000000000000000000000
χ788-808-4-40044-8-4-42000-6644-20000000000200-66-20000000000000000000000000000000000000000000000000
χ798-80-48800-8-84-4-480000044-80000000000-4000040000000000000000000000000000000000000000000000000
χ808-80-48-400-844-42-4000004-24000000006i−6i20000-200006i−6i0000000000000000000000000000000000000000000
χ818-80-48-400-844-42-4000004-2400000000−6i6i20000-20000−6i6i0000000000000000000000000000000000000000000
χ828-80-4-48004-842-4-400000-2440000006i−6i0020000-20000006i−6i00000000000000000000000000000000000000000
χ838-80-4-48004-842-4-400000-244000000−6i6i0020000-2000000−6i6i00000000000000000000000000000000000000000
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).