Finite Group Databasebeta

← Group #11771959

Character table — Group #11771959

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11112244444444444444448888888888888888888888888883636363672727272727272727272
order122222336666666666666644412121212121212121212121212121212121212121212121244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111-1-1-1-1-1-1ii−i−iii−i−i
χ41111111111111111111111111111111111111111111111111-1-1-1-1-1-1−i−iii−i−iii
χ51111111111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ61111111111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ71111111111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii
χ81111111111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i
χ9222222222222222222222200-2-2-2-2-2-2-2-2-200000000000000002-2-220000000000
χ10222222222222222222222200-2-2-2-2-2-2-2-2-20000000000000000-222-20000000000
χ112-22-22-222222222-2-2-2-2-2-2-2-2000000000000000000000000000200-2002−22−20000
χ122-22-22-222222222-2-2-2-2-2-2-2-2000000000000000000000000000200-200−22−220000
χ132-22-22-222222222-2-2-2-2-2-2-2-2000000000000000000000000000-200200−i2i2i2−i20000
χ142-22-22-222222222-2-2-2-2-2-2-2-2000000000000000000000000000-200200i2−i2−i2i20000
χ152-22-2-222222-2-2-2-22222-2-2-2-200000000000000000000000000002i−2i00000001−i−1+i1+i−1−i
χ162-22-2-222222-2-2-2-22222-2-2-2-200000000000000000000000000002i−2i0000000−1+i1−i−1−i1+i
χ172-22-2-222222-2-2-2-22222-2-2-2-20000000000000000000000000000−2i2i00000001+i−1−i1−i−1+i
χ182-22-2-222222-2-2-2-22222-2-2-2-20000000000000000000000000000−2i2i0000000−1−i1+i−1+i1−i
χ194444441-21-211-2-211-2-21-21-200-42222-1-1-1-1000000003333-3-3-3-300000000000000
χ204444441-21-211-2-211-2-21-21-200-42222-1-1-1-100000000-3-3-3-3333300000000000000
χ214444441-21-211-2-211-2-21-21-2444-2-2-2-21111-2-2-2-2-2-2-2-21111111100000000000000
χ224444441-21-211-2-211-2-21-21-2-4-44-2-2-2-2111122222222-1-1-1-1-1-1-1-100000000000000
χ23444444-21-21-2-211-2-211-21-2100-4-1-1-1-122223333-3-3-3-30000000000000000000000
χ24444444-21-21-2-211-2-211-21-2100-4-1-1-1-12222-3-3-3-333330000000000000000000000
χ25444444-21-21-2-211-2-211-21-214441111-2-2-2-211111111-2-2-2-2-2-2-2-200000000000000
χ26444444-21-21-2-211-2-211-21-21-4-441111-2-2-2-2-1-1-1-1-1-1-1-12222222200000000000000
χ274444-4-41-21-2-1-122-1-1221-21-2000000033-3-30000−2i3−2i32i32i3−i3−i3i3i3−i3−i3i3i300000000000000
χ284444-4-41-21-2-1-122-1-1221-21-2000000033-3-300002i32i3−2i3−2i3i3i3−i3−i3i3i3−i3−i300000000000000
χ294444-4-41-21-2-1-122-1-1221-21-20000000-3-333−2i3−2i32i32i30000−i3−i3i3i3i3i3−i3−i300000000000000
χ304444-4-41-21-2-1-122-1-1221-21-20000000-3-3332i32i3−2i3−2i30000i3i3−i3−i3−i3−i3i3i300000000000000
χ314444-4-44444-4-4-4-4-4-4-4-4444400000000000000000000000000000000000000000
χ324444-4-4-21-2122-1-122-1-1-21-2100033-3-30000−i3−i3i3i3−i3−i3i3i32i32i3−2i3−2i3000000000000000000
χ334444-4-4-21-2122-1-122-1-1-21-2100033-3-30000i3i3−i3−i3i3i3−i3−i3−2i3−2i32i32i3000000000000000000
χ344444-4-4-21-2122-1-122-1-1-21-21000-3-3330000−i3−i3i3i3i3i3−i3−i30000−2i3−2i32i32i300000000000000
χ354444-4-4-21-2122-1-122-1-1-21-21000-3-3330000i3i3−i3−i3−i3−i3i3i300002i32i3−2i3−2i300000000000000
χ3644-4-40044-4-400000000-4-44400000000000000000000000000000002i−2i00000000
χ3744-4-40044-4-400000000-4-4440000000000000000000000000000000−2i2i00000000
χ384-4-44001-2-123-3003-3001-2-122i−2i000−2i32i3−i3i3−i3i3−2ζ142ζ142ζ22−2ζ22−2ζ142ζ142ζ22−2ζ22ζ14+3ζ22−ζ14−3ζ22−3ζ14−ζ223ζ14+ζ22i−ii−i00000000000000
χ394-4-44001-2-123-3003-3001-2-122i−2i0002i3−2i3i3−i3i3−i3−2ζ222ζ222ζ14−2ζ14−2ζ222ζ222ζ14−2ζ143ζ14+ζ22−3ζ14−ζ22−ζ14−3ζ22ζ14+3ζ22i−ii−i00000000000000
χ404-4-44001-2-123-3003-3001-2-12−2i2i000−2i32i3−i3i3−i3i32ζ14−2ζ14−2ζ222ζ222ζ14−2ζ14−2ζ222ζ22−ζ14−3ζ22ζ14+3ζ223ζ14+ζ22−3ζ14−ζ22−ii−ii00000000000000
χ414-4-44001-2-123-3003-3001-2-12−2i2i0002i3−2i3i3−i3i3−i32ζ22−2ζ22−2ζ142ζ142ζ22−2ζ22−2ζ142ζ14−3ζ14−ζ223ζ14+ζ22ζ14+3ζ22−ζ14−3ζ22−ii−ii00000000000000
χ424-4-44001-2-12-3300-33001-2-122i−2i0−2i32i300−i3i3i3−i3−2ζ142ζ142ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14i−i−ii3ζ14+ζ22−3ζ14−ζ22ζ14+3ζ22−ζ14−3ζ2200000000000000
χ434-4-44001-2-12-3300-33001-2-122i−2i02i3−2i300i3−i3−i3i3−2ζ222ζ222ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22i−i−iiζ14+3ζ22−ζ14−3ζ223ζ14+ζ22−3ζ14−ζ2200000000000000
χ444-4-44001-2-12-3300-33001-2-12−2i2i0−2i32i300−i3i3i3−i32ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22−2ζ142ζ14−iii−i−3ζ14−ζ223ζ14+ζ22−ζ14−3ζ22ζ14+3ζ2200000000000000
χ454-4-44001-2-12-3300-33001-2-12−2i2i02i3−2i300i3−i3−i3i32ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14−2ζ222ζ22−iii−i−ζ14−3ζ22ζ14+3ζ22−3ζ14−ζ223ζ14+ζ2200000000000000
χ464-4-440044-4-40000000044-4-42i−2i000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i−2i2i00000000000000
χ474-4-440044-4-40000000044-4-4−2i2i0000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i2i−2i00000000000000
χ484-4-4400-212-1003-3003-3-212-12i−2i0−i3i3−i3i32i3−2i300ζ14+3ζ22−ζ14−3ζ22−3ζ14−ζ223ζ14+ζ22i−i−ii−2ζ222ζ222ζ14−2ζ14−2ζ142ζ14−2ζ222ζ2200000000000000
χ494-4-4400-212-1003-3003-3-212-12i−2i0i3−i3i3−i3−2i32i3003ζ14+ζ22−3ζ14−ζ22−ζ14−3ζ22ζ14+3ζ22i−i−ii−2ζ142ζ142ζ22−2ζ22−2ζ222ζ22−2ζ142ζ1400000000000000
χ504-4-4400-212-1003-3003-3-212-1−2i2i0−i3i3−i3i32i3−2i300−ζ14−3ζ22ζ14+3ζ223ζ14+ζ22−3ζ14−ζ22−iii−i2ζ22−2ζ22−2ζ142ζ142ζ14−2ζ142ζ22−2ζ2200000000000000
χ514-4-4400-212-1003-3003-3-212-1−2i2i0i3−i3i3−i3−2i32i300−3ζ14−ζ223ζ14+ζ22ζ14+3ζ22−ζ14−3ζ22−iii−i2ζ14−2ζ14−2ζ222ζ222ζ22−2ζ222ζ14−2ζ1400000000000000
χ524-4-4400-212-100-3300-33-212-12i−2i0−i3i3i3−i300−2i32i3i−i−ii3ζ14+ζ22−3ζ14−ζ22−ζ14−3ζ22ζ14+3ζ22−2ζ142ζ142ζ22−2ζ22−2ζ142ζ14−2ζ222ζ2200000000000000
χ534-4-4400-212-100-3300-33-212-12i−2i0i3−i3−i3i3002i3−2i3i−i−iiζ14+3ζ22−ζ14−3ζ22−3ζ14−ζ223ζ14+ζ22−2ζ222ζ222ζ14−2ζ14−2ζ222ζ22−2ζ142ζ1400000000000000
χ544-4-4400-212-100-3300-33-212-1−2i2i0−i3i3i3−i300−2i32i3−iii−i−3ζ14−ζ223ζ14+ζ22ζ14+3ζ22−ζ14−3ζ222ζ14−2ζ14−2ζ222ζ222ζ14−2ζ142ζ22−2ζ2200000000000000
χ554-4-4400-212-100-3300-33-212-1−2i2i0i3−i3−i3i3002i3−2i3−iii−i−ζ14−3ζ22ζ14+3ζ223ζ14+ζ22−3ζ14−ζ222ζ22−2ζ22−2ζ142ζ142ζ22−2ζ222ζ14−2ζ1400000000000000
χ5688-8-8002-4-246-600-6600-242-400000000000000000000000000000000000000000
χ5788-8-8002-4-24-66006-600-242-400000000000000000000000000000000000000000
χ5888-8-800-424-2006-600-664-2-4200000000000000000000000000000000000000000
χ5988-8-800-424-200-66006-64-2-4200000000000000000000000000000000000000000
χ608-88-88-82-42-422-4-4-2-244-24-2400000000000000000000000000000000000000000
χ618-88-88-8-42-42-4-42244-2-24-24-200000000000000000000000000000000000000000
χ628-88-8-882-42-4-2-24422-4-4-24-2400000000000000000000000000000000000000000
χ638-88-8-88-42-4244-2-2-4-4224-24-200000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.