Finite Group Databasebeta

← Group #13156251

Character table — Group #13156251

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size112222222224444444444444444444448888888888888812122424242424242424242424242424242424242424242424242424363654547272727272727272108
order12233344666333666666661212121212121212121236666612121212121212122446666812121212121212121212121224242424242424248888481212242424248
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1
χ3111111111111111111111111111111111111111111111111-111111-1-11-1-1111-1-1-1-111111111-1-1-1-11-111-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-11111-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ51111111111111111111111111111111111111111111111-1-11-1-1-1-1111-111-1-1-111111111111111-1-1-1-1-1-1-1-111-1
χ61111111111111111111111111111111111111111111111-1-11-1-1-1-1-111-111-1-1-11111-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-11
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-11-1-111-1-11
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
χ9222222-2-222222222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-200000000000000000000000000002i−2i000000002i−2i0
χ10222222-2-222222222222222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-20000000000000000000000000000−2i2i00000000−2i2i0
χ1122222-12222-12-1-122-122-1-122-1-1-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12202-1-1-1200200-1-1-1000022-1-1-1-1-1-1000020-1-100000
χ1222222-12222-12-1-122-122-1-122-1-1-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12202-1-1-1-200200-1-1-10000-2-21111110000-201100000
χ1322222-12222-12-1-122-122-1-122-1-1-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-20-2111200-200111000022-1-1-1-1-1-10000-201100000
χ1422222-12222-12-1-122-122-1-122-1-1-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-20-2111-200-2001110000-2-2111111000020-1-100000
χ152222-12222-12-12-12-12-1-12-1-1-12-1-122222-1-12-1-1-1-12-1-1-1-1-1-1-1222-12-1-1022-1-1-12-1-1-1-1-1-10000000000000200-1-1000
χ162222-12222-12-12-12-12-1-12-1-1-12-1-122222-1-12-1-1-1-12-1-1-1-1-1-1-122-2-12-1-10-2-2-1112-1-111110000000000000-20011000
χ172222-12222-12-12-12-12-1-12-1-1-12-1-122222-1-12-1-1-1-12-1-1-1-1-1-1-1-2-221-2110221-1-1-211-1-1-1-10000000000000-20011000
χ182222-12222-12-12-12-12-1-12-1-1-12-1-122222-1-12-1-1-1-12-1-1-1-1-1-1-1-2-2-21-2110-2-2111-21111110000000000000200-1-1000
χ19222-12222-122-1-12-122-1-1-12-12222-12-1-1-12-1-12-1-1-1-12-1-1-1-1-1-100200002-1-1022000-1-1-1-1-1-122-1-1-1-12200000000-1-10
χ20222-12222-122-1-12-122-1-1-12-12222-12-1-1-12-1-12-1-1-1-12-1-1-1-1-1-10020000-2-1-1022000-1-1-1-111-2-21111-2-200000000110
χ21222-12222-122-1-12-122-1-1-12-12222-12-1-1-12-1-12-1-1-1-12-1-1-1-1-1-100-200002110-2-20001111-1-122-1-1-1-1-2-200000000110
χ22222-12222-122-1-12-122-1-1-12-12222-12-1-1-12-1-12-1-1-1-12-1-1-1-1-1-100-20000-2110-2-2000111111-2-211112200000000-1-10
χ23222-122-2-2-122-1-12-122-1-1-12-1-2-2-2-21-2111-2-1-12-1-1-11-211111100000000−i3i3000000−i3−i3i3i33−30033−3−32i−2i00000000−ii0
χ24222-122-2-2-122-1-12-122-1-1-12-1-2-2-2-21-2111-2-1-12-1-1-11-211111100000000−i3i3000000−i3−i3i3i3−3300−3−333−2i2i00000000i−i0
χ25222-122-2-2-122-1-12-122-1-1-12-1-2-2-2-21-2111-2-1-12-1-1-11-211111100000000i3−i3000000i3i3−i3−i33−30033−3−3−2i2i00000000i−i0
χ26222-122-2-2-122-1-12-122-1-1-12-1-2-2-2-21-2111-2-1-12-1-1-11-211111100000000i3−i3000000i3i3−i3−i3−3300−3−3332i−2i00000000−ii0
χ2722-22222-2222222-2-2-2-2-2222-2-2-2-22222-222-2-2-2-22-222-222-2-22-202222000-200-2-2-20000000000000000000000000
χ2822-22222-2222222-2-2-2-2-2222-2-2-2-22222-222-2-2-2-22-222-222-2-2-220-2-2-2-20002002220000000000000000000000000
χ2922-2222-22222222-2-2-2-2-22222222-2-2-2-22-22-2-2-2-222-2-22-2-2220000000000000000000000000000002200000000-2
χ3022-2222-22222222-2-2-2-2-22222222-2-2-2-22-22-2-2-2-222-2-22-2-222000000000000000000000000000000-2-2000000002
χ3122-222-12-222-12-1-1-2-21-2-2-1-12-21112-1-1-1-22-11111-11-12-2-1-1112-202-1-1-1000-200111000000−i3i3−i3i3−i3i3000000−i3i300000
χ3222-222-12-222-12-1-1-2-21-2-2-1-12-21112-1-1-1-22-11111-11-12-2-1-1112-202-1-1-1000-200111000000i3−i3i3−i3i3−i3000000i3−i300000
χ3322-222-12-222-12-1-1-2-21-2-2-1-12-21112-1-1-1-22-11111-11-12-2-1-111-220-2111000200-1-1-1000000−i3i3−i3i3−i3i3000000i3−i300000
χ3422-222-12-222-12-1-1-2-21-2-2-1-12-21112-1-1-1-22-11111-11-12-2-1-111-220-2111000200-1-1-1000000i3−i3i3−i3i3−i3000000−i3i300000
χ3522-22-122-22-12-12-1-21-2112-1-11-2112222-2-1-1-2111-1-2-1-11-1-1112-20-12-1-10001−i3i3-211−i3i3−i3i30000000000000000−i3i3000
χ3622-22-122-22-12-12-1-21-2112-1-11-2112222-2-1-1-2111-1-2-1-11-1-1112-20-12-1-10001i3−i3-211i3−i3i3−i30000000000000000i3−i3000
χ3722-22-122-22-12-12-1-21-2112-1-11-2112222-2-1-1-2111-1-2-1-11-1-111-2201-211000-1−i3i32-1-1−i3i3−i3i30000000000000000i3−i3000
χ3822-22-122-22-12-12-1-21-2112-1-11-2112222-2-1-1-2111-1-2-1-11-1-111-2201-211000-1i3−i32-1-1i3−i3i3−i30000000000000000−i3i3000
χ3944444-2-4-444-24-2-244-244-2-24-4222-4222-4-4-2-2-2-2-2-222-4-4222200000000000000000000000000000000000000000
χ404444-24-4-44-24-24-24-24-2-24-2-22-422-4-4-4-4-42-24-2-2-2-2-4222222200000000000000000000000000000000000000000
χ414444-2-2444-2-2-2-214-2-2-2-2-21-2-2-2114-2-2-24-21-21111-21-2-21111440-2-211000-200-2110000000000000000000000000
χ424444-2-2444-2-2-2-214-2-2-2-2-21-2-2-2114-2-2-24-21-21111-21-2-21111-4-4022-1-10002002-1-10000000000000000000000000
χ434444-2-2-4-44-2-2-2-214-2-2-2-2-21-222-1-1-4222-421-211112-122-1-1-1-1000003-300000003-30000000000000000000000000
χ444444-2-2-4-44-2-2-2-214-2-2-2-2-21-222-1-1-4222-421-211112-122-1-1-1-100000-330000000-330000000000000000000000000
χ45444-24-244-24-2-21-2-24-2-2-21-2-24-2-2-2-2-211-2411-21111-2-2-2111100000004000000000000-2-2-2-211110000000000000
χ46444-24-244-24-2-21-2-24-2-2-21-2-24-2-2-2-2-211-2411-21111-2-2-211110000000-40000000000002222-1-1-1-10000000000000
χ47444-24-2-4-4-24-2-21-2-24-2-2-21-2-2-422222-1-12-411-2111-1222-1-1-1-10000000000000000000023−2300−3−3330000000000000
χ48444-24-2-4-4-24-2-21-2-24-2-2-21-2-2-422222-1-12-411-2111-1222-1-1-1-100000000000000000000−23230033−3−30000000000000
χ49444-2-2444-2-241-2-2-2-2411-2-21-24-2-2-24-2-2-2-21-2-2111-2-211111100400000-2-20-2-20001111000000000000000000000
χ50444-2-2444-2-241-2-2-2-2411-2-21-24-2-2-24-2-2-2-21-2-2111-2-211111100-40000022022000-1-1-1-1000000000000000000000
χ51444-2-24-4-4-2-241-2-2-2-2411-2-212-4222-422221-2-211122-1-1-1-1-1-100000000−2i32i3000000i3i3−i3−i3000000000000000000000
χ52444-2-24-4-4-2-241-2-2-2-2411-2-212-4222-422221-2-211122-1-1-1-1-1-1000000002i3−2i3000000−i3−i3i3i3000000000000000000000
χ5344-444-2-4444-24-2-2-4-42-4-4-2-244-2-2-2-42224-4-22222-2-22-4422-2-200000000000000000000000000000000000000000
χ5444-44-24-444-24-24-2-42-4224-2-2-24-2-2-4-4-4-442-2-4222-2422-222-2-200000000000000000000000000000000000000000
χ5544-44-2-24-44-2-2-2-21-42222-21-222-1-14-2-2-2-4-212-1-1-1121-2211-1-14-40-2-2110002002-1-10000000000000000000000000
χ5644-44-2-24-44-2-2-2-21-42222-21-222-1-14-2-2-2-4-212-1-1-1121-2211-1-1-44022-1-1000-200-2110000000000000000000000000
χ5744-44-2-2-444-2-2-2-21-42222-21-2-2-211-42224212-1-1-11-2-12-2-1-111000003-30000000-330000000000000000000000000
χ5844-44-2-2-444-2-2-2-21-42222-21-2-2-211-42224212-1-1-11-2-12-2-1-11100000-3300000003-30000000000000000000000000
χ5944-4-2444-4-244-2-242-4-422-24-2-4-4-4-4-24-2-224-22-422-224-22-2-22200000000000000000000000000000000000000000
χ6044-4-244-44-244-2-242-4-422-24-244442-422-2-4-22-422-2-2-42-222-2-200000000000000000000000000000000000000000
χ6144-4-24-24-4-24-2-21-22-42221-2-2-4222-2-211241-12-1-11-1-2-2211-1-10000000000000000000000−2i32i3i3−i3i3−i30000000000000
χ6244-4-24-24-4-24-2-21-22-42221-2-2-4222-2-211241-12-1-11-1-2-2211-1-100000000000000000000002i3−2i3−i3i3−i3i30000000000000
χ6344-4-24-2-44-24-2-21-22-42221-2-24-2-2-222-1-1-2-41-12-1-11122-2-1-1110000000000000000000000003i−3i−3i3i0000000000000
χ6444-4-24-2-44-24-2-21-22-42221-2-24-2-2-222-1-1-2-41-12-1-11122-2-1-111000000000000000000000000−3i3i3i−3i0000000000000
χ6544-4-2-244-4-2-241-2-222-4-1-1-2-212-422-24-2-22-2122-1-112-21-111-1-100000000000−2i32i3000i3−i3i3−i3000000000000000000000
χ6644-4-2-244-4-2-241-2-222-4-1-1-2-212-422-24-2-22-2122-1-112-21-111-1-1000000000002i3−2i3000−i3i3−i3i3000000000000000000000
χ6744-4-2-24-44-2-241-2-222-4-1-1-2-21-24-2-22-422-22122-1-11-22-11-1-11100000000000000003-3-33000000000000000000000
χ6844-4-2-24-44-2-241-2-222-4-1-1-2-21-24-2-22-422-22122-1-11-22-11-1-1110000000000000000-333-3000000000000000000000
χ694-4044400-4-4-444400000-4-4-4000000000040000-40000000000000000000000000000000000000022−22000000000
χ704-4044400-4-4-444400000-4-4-4000000000040000-400000000000000000000000000000000000000−2222000000000
χ71888-4-4-488-4-4-4222-4-4-422222-4-422-4-422-4-4-122-1-1-12222-1-1-1-100000000000000000000000000000000000000000
χ72888-4-4-4-8-8-4-4-4222-4-4-42222244-2-244-2-244-122-1-1-1-2-2-2-2111100000000000000000000000000000000000000000
χ7388-8-4-4-48-8-4-4-4222444-2-222244-2-2-4-4224-4-1-2-211-1-222-2-1-11100000000000000000000000000000000000000000
χ7488-8-4-4-4-88-4-4-4222444-2-2222-4-42244-2-2-44-1-2-211-12-2-2211-1-100000000000000000000000000000000000000000
χ758-8088-400-8-848-4-40000044-80000000000-4000040000000000000000000000000000000000000000000000000
χ768-808-4800-84-8-48-400000-8440000000000-4000040000000000000000000000000000000000000000000000000
χ778-808-4-400-844-4-42000004-24006i−6i00000020000-20000006i−6i00000000000000000000000000000000000000000
χ788-808-4-400-844-4-42000004-2400−6i6i00000020000-2000000−6i6i00000000000000000000000000000000000000000
χ798-80-488004-8-8-4-48000004-840000000000-4000040000000000000000000000000000000000000000000000000
χ808-80-48-4004-84-42-400000-2440000006i−6i0020000-200006i−6i0000000000000000000000000000000000000000000
χ818-80-48-4004-84-42-400000-244000000−6i6i0020000-20000−6i6i0000000000000000000000000000000000000000000
χ828-80-4-480044-82-4-40006-644-200000000002006-6-20000000000000000000000000000000000000000000000000
χ838-80-4-480044-82-4-4000-6644-20000000000200-66-20000000000000000000000000000000000000000000000000
χ848-80-4-4-4004442220006-6-2-2-2006i−6i006i−6i00-100-3310000−3i3i−3i3i00000000000000000000000000000000000000000
χ858-80-4-4-4004442220006-6-2-2-200−6i6i00−6i6i00-100-33100003i−3i3i−3i00000000000000000000000000000000000000000
χ868-80-4-4-400444222000-66-2-2-2006i−6i00−6i6i00-1003-3100003i−3i−3i3i00000000000000000000000000000000000000000
χ878-80-4-4-400444222000-66-2-2-200−6i6i006i−6i00-1003-310000−3i3i3i−3i00000000000000000000000000000000000000000

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