Finite Group Databasebeta

← Group #101760

Character table — Group #101760

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222222244444444444444444444444444444444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1ii−i−iii−i−i1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-111-1-1ii−i−iii−i−i-1-1-1-11111−i−iii−i−iii-11
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-111-1-1-111ii−i−i−i−iii1111-1-1-1-1ii−i−i−i−iii-11
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-111-1-1-111ii−i−i−i−iii-1-1-1-11111−i−iiiii−i−i1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-111-1-1-111−i−iiiii−i−i1111-1-1-1-1−i−iiiii−i−i-11
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-111-1-1-111−i−iiiii−i−i-1-1-1-11111ii−i−i−i−iii1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−iii−i−iii1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-111-1-1−i−iii−i−iii-1-1-1-11111ii−i−iii−i−i-11
χ1722222222222222-2-222-2-222-2-20000000022222222-2-20000-200000000-2-2-2-2000000000000000000
χ1822222222222222-2-222-2-222-2-200000000-2-2-2-2-2-2-2-2-2-20000-2000000002222000000000000000000
χ19222222222222-2-222-2-222-2-2222222222200000000-2-20000-20000-2-2-2-20000000000000000000000
χ20222222222222-2-222-2-222-2-222-2-2-2-2-2-2-2-200000000-2-20000-2000022220000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222222-2-2-2-200000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022-2-2-2-22222200000000000000000000000000
χ2322222222-2-2-2-222222222-2-2-2-200000000000000002222-2-2-2-2-22200000000000000000000000000
χ2422222222-2-2-2-222222222-2-2-2-2000000000000000022-2-222-222-2-200000000000000000000000000
χ2522222222-2-2-2-222-2-222-2-2-2-2222i2i2i2i−2i−2i−2i−2i00000000-2-2000020000−2i−2i2i2i0000000000000000000000
χ2622222222-2-2-2-222-2-222-2-2-2-222−2i−2i−2i−2i2i2i2i2i00000000-2-20000200002i2i−2i−2i0000000000000000000000
χ2722222222-2-2-2-2-2-222-2-22222-2-2000000002i2i2i2i−2i−2i−2i−2i-2-20000200000000−2i−2i2i2i000000000000000000
χ2822222222-2-2-2-2-2-222-2-22222-2-200000000−2i−2i−2i−2i2i2i2i2i-2-200002000000002i2i−2i−2i000000000000000000
χ29222-22-2-2-222-2-2002200-2-2002-222-2-222-2-200000000000000000000000000022−2−222−2−22−22−2000000
χ30222-22-2-2-222-2-2002200-2-2002-222-2-222-2-2000000000000000000000000000−2−222−2−222−22−22000000
χ31222-22-2-2-222-2-2002200-2-2002-2-2-222-2-22200000000000000000000000000022−2−222−2−2−22−22000000
χ32222-22-2-2-222-2-2002200-2-2002-2-2-222-2-222000000000000000000000000000−2−222−2−2222−22−2000000
χ33222-22-2-2-2-2-22200-2-20022002-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000022−2−2−2−222i2−i2−i2i2000000
χ34222-22-2-2-2-2-22200-2-20022002-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000−2−22222−2−2−i2i2i2−i2000000
χ35222-22-2-2-2-2-22200-2-20022002-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000022−2−2−2−222−i2i2i2−i2000000
χ36222-22-2-2-2-2-22200-2-20022002-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000−2−22222−2−2i2−i2−i2i2000000
χ3722-22-22-2-22-22-22200-2-2002-2000000000022-2-222-2-200000000000000000002−22−22−22−200002−22−200
χ3822-22-22-2-22-22-22200-2-2002-2000000000022-2-222-2-20000000000000000000−22−22−22−220000−22−2200
χ3922-22-22-2-22-22-22200-2-2002-20000000000-2-222-2-22200000000000000000002−22−22−22−20000−22−2200
χ4022-22-22-2-22-22-22200-2-2002-20000000000-2-222-2-2220000000000000000000−22−22−22−2200002−22−200
χ4122-22-22-2-2-22-22-2-20022002-200000000002i2i−2i−2i−2i−2i2i2i00000000000000000002−22−2−22−220000i2−i2−i2i200
χ4222-22-22-2-2-22-22-2-20022002-200000000002i2i−2i−2i−2i−2i2i2i0000000000000000000−22−222−22−20000−i2i2i2−i200
χ4322-22-22-2-2-22-22-2-20022002-20000000000−2i−2i2i2i2i2i−2i−2i00000000000000000002−22−2−22−220000−i2i2i2−i200
χ4422-22-22-2-2-22-22-2-20022002-20000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000−22−222−22−20000i2−i2−i2i200
χ452-222-2-2-2200002i−2i2i−2i2i−2i2i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i2-2002i−2i02-2001+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000000000
χ462-222-2-2-2200002i−2i2i−2i2i−2i2i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-200−2i2i0-22001+i−1−i1−i−1+i−1−i1+i−1+i1−i000000000000000000
χ472-222-2-2-2200002i−2i2i−2i2i−2i2i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i2-200−2i2i0-2200−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000000000000000
χ482-222-2-2-2200002i−2i2i−2i2i−2i2i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-2002i−2i02-200−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000000000
χ492-222-2-2-2200002i−2i−2i2i2i−2i−2i2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i-222i−2i000002-2−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000000000
χ502-222-2-2-2200002i−2i−2i2i2i−2i−2i2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i-22−2i2i00000-22−1+i1−i−1−i1+i1+i−1−i1−i−1+i000000000000000000
χ512-222-2-2-2200002i−2i−2i2i2i−2i−2i2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i-22−2i2i00000-221−i−1+i1+i−1−i−1−i1+i−1+i1−i000000000000000000
χ522-222-2-2-2200002i−2i−2i2i2i−2i−2i2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i-222i−2i000002-21−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000000000
χ532-222-2-2-220000−2i2i2i−2i−2i2i2i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i-22−2i2i000002-2−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000000000
χ542-222-2-2-220000−2i2i2i−2i−2i2i2i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i-222i−2i00000-22−1−i1+i−1+i1−i1−i−1+i1+i−1−i000000000000000000
χ552-222-2-2-220000−2i2i2i−2i−2i2i2i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i-222i−2i00000-221+i−1−i1−i−1+i−1+i1−i−1−i1+i000000000000000000
χ562-222-2-2-220000−2i2i2i−2i−2i2i2i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i-22−2i2i000002-21+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000000000
χ572-222-2-2-220000−2i2i−2i2i−2i2i−2i2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i2-200−2i2i02-2001−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000000000
χ582-222-2-2-220000−2i2i−2i2i−2i2i−2i2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-2002i−2i0-22001−i−1+i1+i−1−i−1+i1−i−1−i1+i000000000000000000
χ592-222-2-2-220000−2i2i−2i2i−2i2i−2i2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i2-2002i−2i0-2200−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000000000000000
χ602-222-2-2-220000−2i2i−2i2i−2i2i−2i2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-200−2i2i02-200−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000000000
χ61444-44-4-4-444-4-400-4-4004400-4400000000000000000000000000000000000000000000000000000
χ62444-44-4-4-4-4-444004400-4-400-4400000000000000000000000000000000000000000000000000000
χ6344-44-44-4-44-44-4-4-4004400-440000000000000000000000000000000000000000000000000000000
χ6444-44-44-4-4-44-444400-4-400-440000000000000000000000000000000000000000000000000000000
χ6544-4-4-4-4444-4-44000000000000000000000000000000000000000000000002-2-222-2-220000000000
χ6644-4-4-4-4444-4-4400000000000000000000000000000000000000000000000-222-2-222-20000000000
χ6744-4-4-4-444-444-4000000000000000000000000000000000000000000000002-2-22-222-20000000000
χ6844-4-4-4-444-444-400000000000000000000000000000000000000000000000-222-22-2-220000000000
χ694-44-4-444-40000004i−4i00−4i4i00002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i000000000000000000000000000000000000000000000
χ704-44-4-444-40000004i−4i00−4i4i0000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000000000000
χ714-44-4-444-4000000−4i4i004i−4i00002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i000000000000000000000000000000000000000000000
χ724-44-4-444-4000000−4i4i004i−4i0000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000000000000
χ734-4-444-44-400004i−4i00−4i4i000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i0000000000000000000000000000000000000
χ744-4-444-44-400004i−4i00−4i4i00000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i0000000000000000000000000000000000000
χ754-4-444-44-40000−4i4i004i−4i000000000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i0000000000000000000000000000000000000
χ764-4-444-44-40000−4i4i004i−4i00000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i0000000000000000000000000000000000000
χ778-8-8-888-88000000000000000000000000000000000000000000000000000000000000000000000

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