Finite Group Databasebeta

← Group #101409

Character table — Group #101409

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444444444444444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111iiii−i−i−i−i-1-11111-1-11-111-1-1ii−i−iii−i−iii−i−i11-1-1ii−i−i11-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-111iiii−i−i−i−i-1-11111-1-11-111-1-1ii−i−iii−i−iii−i−i-1-111−i−iii-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-111iiii−i−i−i−i-1-111-1-1111-1-1-111−i−iiiii−i−i−i−iii11-1-1ii−i−i-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-111iiii−i−i−i−i-1-111-1-1111-1-1-111−i−iiiii−i−i−i−iii-1-111−i−iii11-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-111−i−i−i−iiiii-1-11111-1-11-111-1-1−i−iii−i−iii−i−iii11-1-1−i−iii11-1-1−i−iii
χ1411111111-1-1-1-1-1-1-1-111−i−i−i−iiiii-1-11111-1-11-111-1-1−i−iii−i−iii−i−iii-1-111ii−i−i-1-111ii−i−i
χ1511111111-1-1-1-1-1-1-1-111−i−i−i−iiiii-1-111-1-1111-1-1-111ii−i−i−i−iiiii−i−i11-1-1−i−iii-1-111ii−i−i
χ1611111111-1-1-1-1-1-1-1-111−i−i−i−iiiii-1-111-1-1111-1-1-111ii−i−i−i−iiiii−i−i-1-111ii−i−i11-1-1−i−iii
χ1722222222222222222222222222-2-2-2-20000-2-200000000-2-2-2-200000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000-2-200000000222200000000000000000000
χ19222222222222-2-2-2-2-2-20000000022-2-200002-2000022220000-2-2-2-20000000000000000
χ20222222222222-2-2-2-2-2-20000000022-2-200002-20000-2-2-2-2000022220000000000000000
χ21222222222222-2-2-2-2-2-200000000-2-2222222-22-2-2-2-20000000000000000000000000000
χ22222222222222-2-2-2-2-2-200000000-2-222-2-2-2-2-2222220000000000000000000000000000
χ2322222222-2-2-2-22222-2-200000000222222-2-2-2-2-2-2220000000000000000000000000000
χ2422222222-2-2-2-22222-2-2000000002222-2-222-2-222-2-20000000000000000000000000000
χ2522222222-2-2-2-22222-2-200000000-2-2-2-200002200002i2i−2i−2i0000−2i−2i2i2i0000000000000000
χ2622222222-2-2-2-22222-2-200000000-2-2-2-20000220000−2i−2i2i2i00002i2i−2i−2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2222i2i2i2i−2i−2i−2i−2i22-2-20000-2200000000−2i−2i2i2i00000000000000000000
χ2822222222-2-2-2-2-2-2-2-222−2i−2i−2i−2i2i2i2i2i22-2-20000-22000000002i2i−2i−2i00000000000000000000
χ29222-22-2-2-222-2-222-2-22-222-2-222-2-200000000000000000000000000000000002−22−22−22−2
χ30222-22-2-2-222-2-222-2-22-222-2-222-2-20000000000000000000000000000000000−22−22−22−22
χ31222-22-2-2-222-2-222-2-22-2-2-222-2-22200000000000000000000000000000000002−22−2−22−22
χ32222-22-2-2-222-2-222-2-22-2-2-222-2-2220000000000000000000000000000000000−22−222−22−2
χ33222-22-2-2-2-2-222-2-2222-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000002−2−22i2−i2−i2i2
χ34222-22-2-2-2-2-222-2-2222-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000−222−2−i2i2i2−i2
χ35222-22-2-2-2-2-222-2-2222-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000002−2−22−i2i2i2−i2
χ36222-22-2-2-2-2-222-2-2222-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000−222−2i2−i2−i2i2
χ3722-22-2-2-2200002i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i2i−2i2-2002i−2i002-2001+i−1−i1−i−1+i1+i−1−i1−i−1+i1+i−1−i1−i−1+i0000000000000000
χ3822-22-2-2-2200002i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i2i−2i2-200−2i2i00-2200−1−i1+i−1+i1−i1+i−1−i1−i−1+i−1−i1+i−1+i1−i0000000000000000
χ3922-22-2-2-2200002i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i−2i2i-222i−2i0000002-21−i−1+i1+i−1−i−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000000000
χ4022-22-2-2-2200002i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i−2i2i-22−2i2i000000-22−1+i1−i−1−i1+i−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000000000000000
χ4122-22-2-2-2200002i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i2i−2i2-2002i−2i002-200−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000000000000000
χ4222-22-2-2-2200002i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i2i−2i2-200−2i2i00-22001+i−1−i1−i−1+i−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000000000000000
χ4322-22-2-2-2200002i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i−2i2i-222i−2i0000002-2−1+i1−i−1−i1+i1+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000000000
χ4422-22-2-2-2200002i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i−2i2i-22−2i2i000000-221−i−1+i1+i−1−i1+i−1−i1−i−1+i−1+i1−i−1−i1+i0000000000000000
χ4522-22-2-2-220000−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i2i−2i-222i−2i000000-22−1−i1+i−1+i1−i−1+i1−i−1−i1+i1+i−1−i1−i−1+i0000000000000000
χ4622-22-2-2-220000−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i2i−2i-22−2i2i0000002-21+i−1−i1−i−1+i−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000000000
χ4722-22-2-2-220000−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2i2i2-2002i−2i00-2200−1+i1−i−1−i1+i1−i−1+i1+i−1−i−1+i1−i−1−i1+i0000000000000000
χ4822-22-2-2-220000−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2i2i2-200−2i2i002-2001−i−1+i1+i−1−i1−i−1+i1+i−1−i1−i−1+i1+i−1−i0000000000000000
χ4922-22-2-2-220000−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i2i−2i-222i−2i000000-221+i−1−i1−i−1+i1−i−1+i1+i−1−i−1−i1+i−1+i1−i0000000000000000
χ5022-22-2-2-220000−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i2i−2i-22−2i2i0000002-2−1−i1+i−1+i1−i1−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000000000
χ5122-22-2-2-220000−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2i2i2-2002i−2i00-22001−i−1+i1+i−1−i−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000000000000000
χ5222-22-2-2-220000−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2i2i2-200−2i2i002-200−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000000000000000
χ53444-44-4-4-444-4-4-4-444-4400000000000000000000000000000000000000000000000000
χ54444-44-4-4-4-4-44444-4-4-4400000000000000000000000000000000000000000000000000
χ5544-4-4-444-400004i−4i−4i4i002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i000000000000000000000000000000000000000000
χ5644-4-4-444-400004i−4i−4i4i00−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000000000
χ5744-4-4-444-40000−4i4i4i−4i002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i000000000000000000000000000000000000000000
χ5844-4-4-444-40000−4i4i4i−4i00−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000000000
χ594-4-4444-4-44-44-4000000000000000000000000000000000000000000002-22-200000000
χ604-4-4444-4-44-44-400000000000000000000000000000000000000000000-22-2200000000
χ614-4-4444-4-4-44-44000000000000000000000000000000000000000000002i−2i−2i2i00000000
χ624-4-4444-4-4-44-4400000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ634-4-4-44-4444-4-4400000000000000000000000000000000000000002-22-2000000000000
χ644-4-4-44-4444-4-440000000000000000000000000000000000000000-22-22000000000000
χ654-4-4-44-444-444-400000000000000000000000000000000000000002-2-22000000000000
χ664-4-4-44-444-444-40000000000000000000000000000000000000000-222-2000000000000
χ678-888-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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