Finite Group Databasebeta

← Group #99036

Character table — Group #99036

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444888888884444444488888888888844444444888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1111-1-11-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1111-1-11-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-1-1-1111-1-11-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1-1-1-1111-1-11-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222-2-2-222-2200000000-2-2-2-222-2-200000000000022-2-222-2-2000000000000000000000000
χ182222222222222-2-2-222-2200000000-2-2-2-222-2-2000000000000-2-222-2-222000000000000000000000000
χ1922222222222-2-2222-2-2222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ2022222222222-2-2222-2-222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ2122222222222-2-2-2-2-2-2-2-2200000000-2-222-2-222000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2222222222222-2-2-2-2-2-2-2-2200000000-2-222-2-22200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-2-222222222-222222222-2-222-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2422222222-2-2-222222222-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2522222222-2-2-222-2-2-222-2-20000000022-2-2-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2622222222-2-2-222-2-2-222-2-20000000022-2-2-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-200000000000022-2-2-2-222000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-2000000000000-2-22222-2-2000000000000000000000000
χ292222-2-2-2-20002-22-2-22-2202i2i2i2i−2i−2i−2i−2i002-2000000002i2i−2i−2i0000000000000000000000000000i2−i2i2−i22−22−2
χ302222-2-2-2-20002-22-2-22-2202i2i2i2i−2i−2i−2i−2i002-2000000002i2i−2i−2i0000000000000000000000000000−i2i2−i2i2−22−22
χ312222-2-2-2-20002-22-2-22-220−2i−2i−2i−2i2i2i2i2i002-200000000−2i−2i2i2i0000000000000000000000000000i2−i2i2−i2−22−22
χ322222-2-2-2-20002-22-2-22-220−2i−2i−2i−2i2i2i2i2i002-200000000−2i−2i2i2i0000000000000000000000000000−i2i2−i2i22−22−2
χ332222-2-2-2-2000-222-2-2-22202i2i2i2i−2i−2i−2i−2i00-2200000000−2i−2i2i2i00000000000000000000000000002−2−22−i2i2i2−i2
χ342222-2-2-2-2000-222-2-2-22202i2i2i2i−2i−2i−2i−2i00-2200000000−2i−2i2i2i0000000000000000000000000000−222−2i2−i2−i2i2
χ352222-2-2-2-2000-222-2-2-2220−2i−2i−2i−2i2i2i2i2i00-22000000002i2i−2i−2i00000000000000000000000000002−2−22i2−i2−i2i2
χ362222-2-2-2-2000-222-2-2-2220−2i−2i−2i−2i2i2i2i2i00-22000000002i2i−2i−2i0000000000000000000000000000−222−2−i2i2i2−i2
χ3722-2-222-2-222-20022-200-2-222-2-222-2-22-200000022-2-20000000000000000000000002−22−22−22−200000000
χ3822-2-222-2-222-20022-200-2-222-2-222-2-22-200000022-2-2000000000000000000000000−22−22−22−2200000000
χ3922-2-222-2-222-20022-200-2-2-2-222-2-2222-2000000-2-2220000000000000000000000002−22−2−22−2200000000
χ4022-2-222-2-222-20022-200-2-2-2-222-2-2222-2000000-2-222000000000000000000000000−22−222−22−200000000
χ4122-2-222-2-2-2-220022-200-2222-2-222-2-2-22000000-2-222000000000000000000000000i2−i2−i2i2i2−i2−i2i200000000
χ4222-2-222-2-2-2-220022-200-2222-2-222-2-2-22000000-2-222000000000000000000000000−i2i2i2−i2−i2i2i2−i200000000
χ4322-2-222-2-2-2-220022-200-22-2-222-2-222-2200000022-2-2000000000000000000000000i2−i2−i2i2−i2i2i2−i200000000
χ4422-2-222-2-2-2-220022-200-22-2-222-2-222-2200000022-2-2000000000000000000000000−i2i2i2−i2i2−i2−i2i200000000
χ452-22-22-22-22-2222000-2-20-22−22−22−22−200002-2002−22−22−22−222−2−2002-2002-22−22−22−22−20000000000000000
χ462-22-22-22-22-2222000-2-20-22−22−22−22−200002-2002−22−22−22−222−2−200-2200-22−22−22−22−220000000000000000
χ472-22-22-22-22-2222000-2-20-2−22−22−22−2200002-200−22−22−22−22−2−222002-2002-2−22−22−22−220000000000000000
χ482-22-22-22-22-2222000-2-20-2−22−22−22−2200002-200−22−22−22−22−2−22200-2200-222−22−22−22−20000000000000000
χ492-22-22-22-22-22-2-2000220-22−22−22−22−20000-22002−22−2−22−22−2−2222i−2i002i−2i00i2−i2−i2i2i2−i2−i2i20000000000000000
χ502-22-22-22-22-22-2-2000220-22−22−22−22−20000-22002−22−2−22−22−2−222−2i2i00−2i2i00−i2i2i2−i2−i2i2i2−i20000000000000000
χ512-22-22-22-22-22-2-2000220-2−22−22−22−220000-2200−22−222−22−222−2−22i−2i002i−2i00−i2i2i2−i2−i2i2i2−i20000000000000000
χ522-22-22-22-22-22-2-2000220-2−22−22−22−220000-2200−22−222−22−222−2−2−2i2i00−2i2i00i2−i2−i2i2i2−i2−i2i20000000000000000
χ532-22-22-22-2-22-222000-2-2022−22−22−22−20000-2200−22−222−22−2−2−2222i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ542-22-22-22-2-22-222000-2-2022−22−22−22−20000-2200−22−222−22−2−2−222−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ552-22-22-22-2-22-222000-2-202−22−22−22−220000-22002−22−2−22−2222−2−22i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ562-22-22-22-2-22-222000-2-202−22−22−22−220000-22002−22−2−22−2222−2−2−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ572-22-22-22-2-22-2-2-200022022−22−22−22−200002-200−22−22−22−2222−2−2002-200-222−22−2−22−220000000000000000
χ582-22-22-22-2-22-2-2-200022022−22−22−22−200002-200−22−22−22−2222−2−200-22002-2−22−222−22−20000000000000000
χ592-22-22-22-2-22-2-2-20002202−22−22−22−2200002-2002−22−22−22−2−2−222002-200-22−22−222−22−20000000000000000
χ602-22-22-22-2-22-2-2-20002202−22−22−22−2200002-2002−22−22−22−2−2−22200-22002-22−22−2−22−220000000000000000
χ614444-4-4-4-40004-4-4444-4-400000000000-44000000000000000000000000000000000000000000000000
χ624444-4-4-4-4000-44-444-44-4000000000004-4000000000000000000000000000000000000000000000000
χ6344-4-444-4-444-400-4-44004-400000000-4400000000000000000000000000000000000000000000000000
χ6444-4-444-4-4-4-4400-4-440044000000004-400000000000000000000000000000000000000000000000000
χ6544-4-4-4-444000004-4400-404i4i−4i−4i−4i−4i4i4i0000000000000000000000000000000000000000000000000000
χ6644-4-4-4-444000004-4400-40−4i−4i4i4i4i4i−4i−4i0000000000000000000000000000000000000000000000000000
χ6744-4-4-4-44400000-44-400400000000000000000000000004-44-400000000000000000000000000000000
χ6844-4-4-4-44400000-44-40040000000000000000000000000-44-4400000000000000000000000000000000
χ694-44-4-44-440004-4000-44002i2−2i22i2−2i2−2i22i2−2i22i20000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ704-44-4-44-440004-4000-4400−2i22i2−2i22i22i2−2i22i2−2i2000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ714-44-4-44-44000-440004-4002i2−2i22i2−2i2−2i22i2−2i22i2000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ724-44-4-44-44000-440004-400−2i22i2−2i22i22i2−2i22i2−2i20000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ734-4-444-4-444-4-400000000422−22−222222−22−22220000000022−22−22220000000000000000000000000000000000000000
χ744-4-444-4-444-4-4000000004−222222−22−222222−2200000000−222222−220000000000000000000000000000000000000000
χ754-4-444-4-44-44400000000-422−22−222222−22−222200000000−222222−220000000000000000000000000000000000000000
χ764-4-444-4-44-44400000000-4−222222−22−222222−220000000022−22−22220000000000000000000000000000000000000000
χ774-4-44-444-40000000000002i2−2i2−2i22i2−2i22i22i2−2i20000004i−4i0000000022−22−222200000000000000000000000000000000
χ784-4-44-444-40000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000−4i4i00000000−222222−2200000000000000000000000000000000
χ794-4-44-444-4000000000000−2i22i22i2−2i22i2−2i2−2i22i20000004i−4i00000000−222222−2200000000000000000000000000000000
χ804-4-44-444-4000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000−4i4i0000000022−22−222200000000000000000000000000000000

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