Finite Group Databasebeta

← Group #13156264

Character table — Group #13156264

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size112222222224444444444444444444448888888888888812122424242424242424242424242424242424242424242424242424363654547272727272727272108
order12233344666333666666661212121212121212121236666612121212121212128848121212121212121224242424242424242424242424242424248846812121224248
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1
χ3111111111111111111111111111111111111111111111111-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-11-1-1-111-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-11-1-1-1-11
χ51111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1-11-11-1-1-1-1-1
χ61111111111111111111111111111111111111111111111-1-11-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-11
χ71111111111111111111111111111111111111111111111-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11-1-1-1111
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1
χ9222222-2-222222222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22i−2i00000000002i2i2i2i−2i−2i−2i−2i000000000000000000000
χ10222222-2-222222222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2−2i2i0000000000−2i−2i−2i−2i2i2i2i2i000000000000000000000
χ1122222-1222-122-1-122-1-1-12-1-1-12-12222-1-12-12-1-1-1-12-1-1-1-1-1-1-1002222-1-1-1-1-1-10000000022-1-1-1-1-1-122000-10-100000
χ1222222-1222-122-1-122-1-1-12-1-1-12-12222-1-12-12-1-1-1-12-1-1-1-1-1-1-1002-222-1-1-1-1-1-100000000-2-2111111-2-200010100000
χ1322222-1222-122-1-122-1-1-12-1-1-12-12222-1-12-12-1-1-1-12-1-1-1-1-1-1-100-22-2-21111110000000022-1-1-1-1-1-1-2-200010100000
χ1422222-1222-122-1-122-1-1-12-1-1-12-12222-1-12-12-1-1-1-12-1-1-1-1-1-1-100-2-2-2-211111100000000-2-211111122000-10-100000
χ152222-122222-1-12-12-1222-1-12222-1-1-1-1-1-12-1-1-1-1-1-1-1-122-1-1-1-12202000000002-1-1-12-1-1-1-1-122-1-1-1-100002000-1-1000
χ162222-122222-1-12-12-1222-1-12222-1-1-1-1-1-12-1-1-1-1-1-1-1-122-1-1-1-1220-2000000002-1-1-12-1-1-111-2-211110000-200011000
χ172222-122222-1-12-12-1222-1-12222-1-1-1-1-1-12-1-1-1-1-1-1-1-122-1-1-1-1-2-20200000000-2111-2111-1-122-1-1-1-10000-200011000
χ182222-122222-1-12-12-1222-1-12222-1-1-1-1-1-12-1-1-1-1-1-1-1-122-1-1-1-1-2-20-200000000-2111-211111-2-2111100002000-1-1000
χ192222-12-2-222-1-12-12-1222-1-12-2-2-2111111-2-1-1-1-1-1-111-2-211112i−2i00000000002i−i−i−i−2iiii3−30033−3−300000000−i3i3000
χ202222-12-2-222-1-12-12-1222-1-12-2-2-2111111-2-1-1-1-1-1-111-2-211112i−2i00000000002i−i−i−i−2iiii−3300−3−33300000000i3−i3000
χ212222-12-2-222-1-12-12-1222-1-12-2-2-2111111-2-1-1-1-1-1-111-2-21111−2i2i0000000000−2iiii2i−i−i−i3−30033−3−300000000i3−i3000
χ222222-12-2-222-1-12-12-1222-1-12-2-2-2111111-2-1-1-1-1-1-111-2-21111−2i2i0000000000−2iiii2i−i−i−i−3300−3−33300000000−i3i3000
χ23222-12222-122-1-12-122-1-1-12-12-1222-1-122-1-1-12-1-1-1-12-1-1-1-1-1-12220-1-122-1-1-1-1-12-1-1-12-1-1000000000000002000-1-10
χ24222-12222-122-1-12-122-1-1-12-12-1222-1-122-1-1-12-1-1-1-12-1-1-1-1-1-122-2011-2-21111-12-1-1-12-1-100000000000000-2000110
χ25222-12222-122-1-12-122-1-1-12-12-1222-1-122-1-1-12-1-1-1-12-1-1-1-1-1-1-2-220-1-122-1-1-1-11-2111-21100000000000000-2000110
χ26222-12222-122-1-12-122-1-1-12-12-1222-1-122-1-1-12-1-1-1-12-1-1-1-1-1-1-2-2-2011-2-211111-2111-211000000000000002000-1-10
χ27222-122-2-2-122-1-12-122-1-1-12-1-21-2-2-211-2-21-1-12-1-1-11-21111112i−2i00−i3i300−i3−i3i3i3−i2i−i−ii−2iii0000000000000000003−30
χ28222-122-2-2-122-1-12-122-1-1-12-1-21-2-2-211-2-21-1-12-1-1-11-21111112i−2i00i3−i300i3i3−i3−i3−i2i−i−ii−2iii000000000000000000−330
χ29222-122-2-2-122-1-12-122-1-1-12-1-21-2-2-211-2-21-1-12-1-1-11-2111111−2i2i00−i3i300−i3−i3i3i3i−2iii−i2i−i−i000000000000000000−330
χ30222-122-2-2-122-1-12-122-1-1-12-1-21-2-2-211-2-21-1-12-1-1-11-2111111−2i2i00i3−i300i3i3−i3−i3i−2iii−i2i−i−i0000000000000000003−30
χ3122-22222-2222222-2-2-2-2-2222-2-222-2-2-22222-2-2-2-222-22-222-2-200000000000000000000000000002-200020-200000
χ3222-22222-2222222-2-2-2-2-2222-2-222-2-2-22222-2-2-2-222-22-222-2-20000000000000000000000000000-22000-20200000
χ3322-2222-22222222-2-2-2-2-222222-2-2222-2-2-22-2-2-2-22-22-22-2-2220000000000000000000000000000002200000000-2
χ3422-2222-22222222-2-2-2-2-222222-2-2222-2-2-22-2-2-2-22-22-22-2-222000000000000000000000000000000-2-2000000002
χ3522-222-12-22-122-1-1-2-21112-1-11-2-12-2-2-2-1-12-1-2111-121-11-1-111000000−i3i3−i3i3−i3i30000000000−i3i3−i3i3−i3i32-2000-10100000
χ3622-222-12-22-122-1-1-2-21112-1-11-2-12-2-2-2-1-12-1-2111-121-11-1-111000000−i3i3−i3i3−i3i30000000000i3−i3i3−i3i3−i3-2200010-100000
χ3722-222-12-22-122-1-1-2-21112-1-11-2-12-2-2-2-1-12-1-2111-121-11-1-111000000i3−i3i3−i3i3−i30000000000−i3i3−i3i3−i3i3-2200010-100000
χ3822-222-12-22-122-1-1-2-21112-1-11-2-12-2-2-2-1-12-1-2111-121-11-1-111000000i3−i3i3−i3i3−i30000000000i3−i3i3−i3i3−i32-2000-10100000
χ3944444-2-4-44-244-2-244-2-2-24-2-22-42-4-4-4-422-4-24-2-2-2-2-4222222200000000000000000000000000000000000000000
χ404444-2-2444-2-2-2-214-2-2-2-2-21-2-24-2-2-2-2-21141-21111-21-2-2111100040000000000000000-2-2-2-211110000000000000
χ414444-2-2444-2-2-2-214-2-2-2-2-21-2-24-2-2-2-2-21141-21111-21-2-21111000-400000000000000002222-1-1-1-10000000000000
χ424444-2-2-4-44-2-2-2-214-2-2-2-2-21-22-422222-1-1-41-211112-122-1-1-1-10000000000000000000023−2300−3−3330000000000000
χ434444-2-2-4-44-2-2-2-214-2-2-2-2-21-22-422222-1-1-41-211112-122-1-1-1-100000000000000000000−23230033−3−30000000000000
χ44444-24-244-2-24-21-2-24-211-2-21-2-2-244-2-2-2-2-21-2-2111-2-21111110040-2-2-2-2111100000000000000000000000000000
χ45444-24-244-2-24-21-2-24-211-2-21-2-2-244-2-2-2-2-21-2-2111-2-211111100-402222-1-1-1-100000000000000000000000000000
χ46444-24-2-4-4-2-24-21-2-24-211-2-21222-4-4222221-2-211122-1-1-1-1-1-10000−2i32i300i3i3−i3−i300000000000000000000000000000
χ47444-24-2-4-4-2-24-21-2-24-211-2-21222-4-4222221-2-211122-1-1-1-1-1-100002i3−2i300−i3−i3i3i300000000000000000000000000000
χ48444-2-2444-24-21-2-2-2-24-2-21-2-24-24-2-211-2-2-211-21111-2-2-21111440000000000-2-211-2-211000000000000000000000
χ49444-2-2444-24-21-2-2-2-24-2-21-2-24-24-2-211-2-2-211-21111-2-2-21111-4-4000000000022-1-122-1-1000000000000000000000
χ50444-2-24-4-4-24-21-2-2-2-24-2-21-2-2-42-422-1-122211-2111-1222-1-1-1-14i−4i0000000000−2i−2iii2i2i−i−i000000000000000000000
χ51444-2-24-4-4-24-21-2-2-2-24-2-21-2-2-42-422-1-122211-2111-1222-1-1-1-1−4i4i00000000002i2i−i−i−2i−2iii000000000000000000000
χ5244-444-2-444-244-2-2-4-42224-2-2-242-444422-4-2-4222-2-4-22-222-2-200000000000000000000000000000000000000000
χ5344-44-244-444-2-24-2-42-4-4-4-2-24-4-44-2222-2-24-22222-2-224-4-2-22200000000000000000000000000000000000000000
χ5444-44-24-4444-2-24-2-42-4-4-4-2-2444-42-2-2-222-4-22222-22-2-4422-2-200000000000000000000000000000000000000000
χ5544-44-2-24-44-2-2-2-21-42222-21-22-4-2-222211412-1-1-11-2-1-2211-1-10000000000000000000000−2i32i3i3−i3i3−i30000000000000
χ5644-44-2-24-44-2-2-2-21-42222-21-22-4-2-222211412-1-1-11-2-1-2211-1-100000000000000000000002i3−2i3−i3i3−i3i30000000000000
χ5744-44-2-2-444-2-2-2-21-42222-21-2-2422-2-2-2-1-1-412-1-1-11212-2-1-1110000000000000000000000003i−3i−3i3i0000000000000
χ5844-44-2-2-444-2-2-2-21-42222-21-2-2422-2-2-2-1-1-412-1-1-11212-2-1-111000000000000000000000000−3i3i3i−3i0000000000000
χ5944-4-2444-4-244-2-242-4-422-24-2-4244-42244-2-22-422-2-2-4-22-2-22200000000000000000000000000000000000000000
χ6044-4-244-44-244-2-242-4-422-24-24-2-4-44-2-2-4-42-22-422-2242-222-2-200000000000000000000000000000000000000000
χ6144-4-24-24-4-2-24-21-22-42-1-1-2-2122-24-422-2-2-2122-1-11-221-111-1-1000000−2i32i3i3−i3i3−i300000000000000000000000000000
χ6244-4-24-24-4-2-24-21-22-42-1-1-2-2122-24-422-2-2-2122-1-11-221-111-1-10000002i3−2i3−i3i3−i3i300000000000000000000000000000
χ6344-4-24-2-44-2-24-21-22-42-1-1-2-21-2-22-44-2-2222122-1-112-2-11-1-111000000003-3-3300000000000000000000000000000
χ6444-4-24-2-44-2-24-21-22-42-1-1-2-21-2-22-44-2-2222122-1-112-2-11-1-11100000000-333-300000000000000000000000000000
χ6544-4-2-244-4-24-21-2-222-4221-2-2-424-22-1-1-2-2-21-12-1-1112-2211-1-1000000000000003i−3i003i−3i000000000000000000000
χ6644-4-2-244-4-24-21-2-222-4221-2-2-424-22-1-1-2-2-21-12-1-1112-2211-1-100000000000000−3i3i00−3i3i000000000000000000000
χ6744-4-2-24-44-24-21-2-222-4221-2-24-2-42-2112221-12-1-11-1-22-2-1-111000000000000003-300-33000000000000000000000
χ6844-4-2-24-44-24-21-2-222-4221-2-24-2-42-2112221-12-1-11-1-22-2-1-11100000000000000-33003-3000000000000000000000
χ694-4044400-4-4-444400000-4-4-4000000000040000-40000000000000000000000000000000000000022−22000000000
χ704-4044400-4-4-444400000-4-4-4000000000040000-400000000000000000000000000000000000000−2222000000000
χ71888-4-4-488-4-4-4222-4-4-422222-4-4-4-4-42222-4-122-1-1-12222-1-1-1-100000000000000000000000000000000000000000
χ72888-4-4-4-8-8-4-4-4222-4-4-42222244444-2-2-2-24-122-1-1-1-2-2-2-2111100000000000000000000000000000000000000000
χ7388-8-4-4-48-8-4-4-4222444-2-222244-4-44-2-222-4-1-2-211-12-22-2-1-11100000000000000000000000000000000000000000
χ7488-8-4-4-4-88-4-4-4222444-2-2222-4-444-422-2-24-1-2-211-1-22-2211-1-100000000000000000000000000000000000000000
χ758-8088-400-84-88-4-400000-8440000000000-4000040000000000000000000000000000000000000000000000000
χ768-808-4800-8-84-48-40000044-80000000000-4000040000000000000000000000000000000000000000000000000
χ778-808-4-400-844-4-42000004-2400000006i−6i020000-200006i−6i0000000000000000000000000000000000000000000
χ788-808-4-400-844-4-42000004-240000000−6i6i020000-20000−6i6i0000000000000000000000000000000000000000000
χ798-80-488004-8-8-4-48000004-840000000000-4000040000000000000000000000000000000000000000000000000
χ808-80-48-40044-8-42-40006-644-200000000002006-6-20000000000000000000000000000000000000000000000000
χ818-80-48-40044-8-42-4000-6644-20000000000200-66-20000000000000000000000000000000000000000000000000
χ828-80-4-48004-842-4-400000-244000006i−6i00020000-20000006i−6i00000000000000000000000000000000000000000
χ838-80-4-48004-842-4-400000-24400000−6i6i00020000-2000000−6i6i00000000000000000000000000000000000000000
χ848-80-4-4-4004442220006-6-2-2-2000006i−6i6i−6i0-100-3310000−3i3i−3i3i00000000000000000000000000000000000000000
χ858-80-4-4-4004442220006-6-2-2-200000−6i6i−6i6i0-100-33100003i−3i3i−3i00000000000000000000000000000000000000000
χ868-80-4-4-400444222000-66-2-2-2000006i−6i−6i6i0-1003-3100003i−3i−3i3i00000000000000000000000000000000000000000
χ878-80-4-4-400444222000-66-2-2-200000−6i6i6i−6i0-1003-310000−3i3i3i−3i00000000000000000000000000000000000000000

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