Finite Group Databasebeta

← Group #11771806

Character table — Group #11771806

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11112244444444444444448888888888888888888888888883636363672727272727272727272
order122222336666666666666644412121212121212121212121212121212121212121212121222444444448888
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
χ511111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ611111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ711111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii
χ811111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i
χ92222222222222222222222-200-2-2-2-2-2-2-2-2000000000000000022-2-20000000000
χ102222222222222222222222-200-2-2-2-2-2-2-2-20000000000000000-2-2220000000000
χ112-2-222-222222222-2-2-2-2-2-2-2-2000000000000000000000000000002i−2i001+i−1−i1−i−1+i0000
χ122-2-222-222222222-2-2-2-2-2-2-2-2000000000000000000000000000002i−2i00−1−i1+i−1+i1−i0000
χ132-2-222-222222222-2-2-2-2-2-2-2-200000000000000000000000000000−2i2i001−i−1+i1+i−1−i0000
χ142-2-222-222222222-2-2-2-2-2-2-2-200000000000000000000000000000−2i2i00−1+i1−i−1−i1+i0000
χ152-2-22-222222-2-2-2-2-2-22222-2-20000000000000000000000000002-200000000−i2i2−i2i2
χ162-2-22-222222-2-2-2-2-2-22222-2-20000000000000000000000000002-200000000i2−i2i2−i2
χ172-2-22-222222-2-2-2-2-2-22222-2-2000000000000000000000000000-22000000002−2−22
χ182-2-22-222222-2-2-2-2-2-22222-2-2000000000000000000000000000-2200000000−222−2
χ194444441-21-211-2-21-211-2-21-24441111-2-2-2-211111111-2-2-2-2-2-2-2-200000000000000
χ204444441-21-211-2-21-211-2-21-24-4-41111-2-2-2-2-1-1-1-1-1-1-1-12222222200000000000000
χ214444441-21-211-2-21-211-2-21-2-400-1-1-1-122223333-3-3-3-30000000000000000000000
χ224444441-21-211-2-21-211-2-21-2-400-1-1-1-12222-3-3-3-333330000000000000000000000
χ23444444-21-21-2-211-21-2-211-21444-2-2-2-21111-2-2-2-2-2-2-2-21111111100000000000000
χ24444444-21-21-2-211-21-2-211-214-4-4-2-2-2-2111122222222-1-1-1-1-1-1-1-100000000000000
χ25444444-21-21-2-211-21-2-211-21-4002222-1-1-1-1000000003333-3-3-3-300000000000000
χ26444444-21-21-2-211-21-2-211-21-4002222-1-1-1-100000000-3-3-3-3333300000000000000
χ274444-4-41-21-2-1-1221-2-1-1221-200033-3-3000033−3−333−3−300002323−23−2300000000000000
χ284444-4-41-21-2-1-1221-2-1-1221-200033-3-30000−3−333−3−3330000−23−23232300000000000000
χ294444-4-41-21-2-1-1221-2-1-1221-2000-3-333000033−3−3−3−3332323−23−23000000000000000000
χ304444-4-41-21-2-1-1221-2-1-1221-2000-3-3330000−3−33333−3−3−23−232323000000000000000000
χ314444-4-44444-4-4-4-444-4-4-4-44400000000000000000000000000000000000000000
χ324444-4-4-21-2122-1-1-2122-1-1-21000000033-3-300002323−23−2333−3−3−3−33300000000000000
χ334444-4-4-21-2122-1-1-2122-1-1-21000000033-3-30000−23−232323−3−33333−3−300000000000000
χ344444-4-4-21-2122-1-1-2122-1-1-210000000-3-3332323−23−230000−3−333−3−33300000000000000
χ354444-4-4-21-2122-1-1-2122-1-1-210000000-3-333−23−232323000033−3−333−3−300000000000000
χ3644-4-40044-4-40000-4-400004400000000000000000000000000000002i−2i00000000
χ3744-4-40044-4-40000-4-40000440000000000000000000000000000000−2i2i00000000
χ384-44-4001-2-123-3001-23-300-1202i−2i3−33−30023−23−ζ4−2ζ14+ζ20−2ζ22ζ4+2ζ14−ζ20+2ζ22−ζ4+2ζ14+ζ20+2ζ22ζ4−2ζ14−ζ20−2ζ22i−ii−i−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ2200000000000000
χ394-44-4001-2-123-3001-23-300-1202i−2i−33−3300−2323ζ4−2ζ14−ζ20−2ζ22−ζ4+2ζ14+ζ20+2ζ22ζ4+2ζ14−ζ20+2ζ22−ζ4−2ζ14+ζ20−2ζ22i−ii−iζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ2200000000000000
χ404-44-4001-2-123-3001-23-300-120−2i2i3−33−30023−23ζ4+2ζ14−ζ20+2ζ22−ζ4−2ζ14+ζ20−2ζ22ζ4−2ζ14−ζ20−2ζ22−ζ4+2ζ14+ζ20+2ζ22−ii−iiζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ2200000000000000
χ414-44-4001-2-123-3001-23-300-120−2i2i−33−3300−2323−ζ4+2ζ14+ζ20+2ζ22ζ4−2ζ14−ζ20−2ζ22−ζ4−2ζ14+ζ20−2ζ22ζ4+2ζ14−ζ20+2ζ22−ii−ii−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ2200000000000000
χ424-44-4001-2-12-33001-2-3300-1202i−2i3−3−3323−2300−iii−iζ4+2ζ14−ζ20+2ζ22−ζ4−2ζ14+ζ20−2ζ22−ζ4+2ζ14+ζ20+2ζ22ζ4−2ζ14−ζ20−2ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ2200000000000000
χ434-44-4001-2-12-33001-2-3300-1202i−2i−333−3−232300−iii−i−ζ4+2ζ14+ζ20+2ζ22ζ4−2ζ14−ζ20−2ζ22ζ4+2ζ14−ζ20+2ζ22−ζ4−2ζ14+ζ20−2ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ2200000000000000
χ444-44-4001-2-12-33001-2-3300-120−2i2i3−3−3323−2300i−i−ii−ζ4−2ζ14+ζ20−2ζ22ζ4+2ζ14−ζ20+2ζ22ζ4−2ζ14−ζ20−2ζ22−ζ4+2ζ14+ζ20+2ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ2200000000000000
χ454-44-4001-2-12-33001-2-3300-120−2i2i−333−3−232300i−i−iiζ4−2ζ14−ζ20−2ζ22−ζ4+2ζ14+ζ20+2ζ22−ζ4−2ζ14+ζ20−2ζ22ζ4+2ζ14−ζ20+2ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ2200000000000000
χ464-44-40044-4-40000440000-4-402i−2i000000002i−2i−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i00000000000000
χ474-44-40044-4-40000440000-4-40−2i2i00000000−2i2i2i−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i00000000000000
χ484-44-400-212-1003-3-21003-32-102i−2i0023−233−3−33−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−2ζ14−ζ20−2ζ22−ζ4+2ζ14+ζ20+2ζ22ζ4+2ζ14−ζ20+2ζ22−ζ4−2ζ14+ζ20−2ζ22−iii−i00000000000000
χ494-44-400-212-1003-3-21003-32-102i−2i00−2323−333−3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−2ζ14+ζ20−2ζ22ζ4+2ζ14−ζ20+2ζ22−ζ4+2ζ14+ζ20+2ζ22ζ4−2ζ14−ζ20−2ζ22−iii−i00000000000000
χ504-44-400-212-1003-3-21003-32-10−2i2i0023−233−3−33ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+2ζ14+ζ20+2ζ22ζ4−2ζ14−ζ20−2ζ22−ζ4−2ζ14+ζ20−2ζ22ζ4+2ζ14−ζ20+2ζ22i−i−ii00000000000000
χ514-44-400-212-1003-3-21003-32-10−2i2i00−2323−333−3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+2ζ14−ζ20+2ζ22−ζ4−2ζ14+ζ20−2ζ22ζ4−2ζ14−ζ20−2ζ22−ζ4+2ζ14+ζ20+2ζ22i−i−ii00000000000000
χ524-44-400-212-100-33-2100-332-102i−2i23−2300−33−33−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−iii−iζ4−2ζ14−ζ20−2ζ22−ζ4+2ζ14+ζ20+2ζ22ζ4+2ζ14−ζ20+2ζ22−ζ4−2ζ14+ζ20−2ζ2200000000000000
χ534-44-400-212-100-33-2100-332-102i−2i−2323003−33−3ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22−iii−i−ζ4−2ζ14+ζ20−2ζ22ζ4+2ζ14−ζ20+2ζ22−ζ4+2ζ14+ζ20+2ζ22ζ4−2ζ14−ζ20−2ζ2200000000000000
χ544-44-400-212-100-33-2100-332-10−2i2i23−2300−33−33ζ4−ζ14−ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22i−i−ii−ζ4+2ζ14+ζ20+2ζ22ζ4−2ζ14−ζ20−2ζ22−ζ4−2ζ14+ζ20−2ζ22ζ4+2ζ14−ζ20+2ζ2200000000000000
χ554-44-400-212-100-33-2100-332-10−2i2i−2323003−33−3−ζ4−ζ14+ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22ζ4+ζ14−ζ20+ζ22−ζ4−ζ14+ζ20−ζ22−ζ4+ζ14+ζ20+ζ22ζ4−ζ14−ζ20−ζ22i−i−iiζ4+2ζ14−ζ20+2ζ22−ζ4−2ζ14+ζ20−2ζ22ζ4−2ζ14−ζ20−2ζ22−ζ4+2ζ14+ζ20+2ζ2200000000000000
χ5688-8-8002-4-246-600-24-66002-400000000000000000000000000000000000000000
χ5788-8-8002-4-24-6600-246-6002-400000000000000000000000000000000000000000
χ5888-8-800-424-2006-64-200-66-4200000000000000000000000000000000000000000
χ5988-8-800-424-200-664-2006-6-4200000000000000000000000000000000000000000
χ608-8-888-82-42-422-4-4-24-2-244-2400000000000000000000000000000000000000000
χ618-8-888-8-42-42-4-4224-244-2-24-200000000000000000000000000000000000000000
χ628-8-88-882-42-4-2-244-2422-4-4-2400000000000000000000000000000000000000000
χ638-8-88-88-42-4244-2-24-2-4-4224-200000000000000000000000000000000000000000

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