Finite Group Databasebeta

← Group #99034

Character table — Group #99034

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444888888884444444488888888888822224444888888888888888888888888
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
χ911111111-1-1-1-1-1111-1-11-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1111-1-11-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-1-1-1111-1-11-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1-1-1-1111-1-11-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222-2-2-222-220000000022-2-2-2-2-2-20000000000002222-2-2-2-2000000000000000000000000
χ182222222222222-2-2-222-220000000022-2-2-2-2-2-2000000000000-2-2-2-22222000000000000000000000000
χ1922222222222-2-2222-2-22222222222-2-2-2-222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2022222222222-2-2222-2-222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-2222200000000000000000000000000000000
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
χ2322222222-2-2-222222222-222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2422222222-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
χ2522222222-2-2-222-2-2-222-2-200000000-2-22222-2-2000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2622222222-2-2-222-2-2-222-2-200000000-2-22222-2-200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-2222200000000000022-2-2-2-222000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-22222000000000000-2-22222-2-2000000000000000000000000
χ292222-2-2-2-222-222000-2-20-22222−2−2−2−22-200000022−2−222−2−222−2−22-22-200002−22−22−22−20000000000000000
χ302222-2-2-2-222-222000-2-20-22222−2−2−2−22-200000022−2−222−2−222−2−2-22-220000−22−22−22−220000000000000000
χ312222-2-2-2-222-222000-2-20-2−2−2−2−222222-2000000−2−222−2−222−2−2222-22-20000−22−22−22−220000000000000000
χ322222-2-2-2-222-222000-2-20-2−2−2−2−222222-2000000−2−222−2−222−2−222-22-2200002−22−22−22−20000000000000000
χ332222-2-2-2-222-2-2-2000220-22222−2−2−2−2-22000000−2−22222−2−2−2−22200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i20000000000000000
χ342222-2-2-2-222-2-2-2000220-22222−2−2−2−2-22000000−2−22222−2−2−2−2220000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i20000000000000000
χ352222-2-2-2-222-2-2-2000220-2−2−2−2−22222-2200000022−2−2−2−22222−2−200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i20000000000000000
χ362222-2-2-2-222-2-2-2000220-2−2−2−2−22222-2200000022−2−2−2−22222−2−20000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i20000000000000000
χ372222-2-2-2-2-2-2222000-2-2022222−2−2−2−2-22000000−2−222−2−22222−2−200002i−2i−2i2ii2−i2−i2i2−i2i2i2−i20000000000000000
χ382222-2-2-2-2-2-2222000-2-2022222−2−2−2−2-22000000−2−222−2−22222−2−20000−2i2i2i−2i−i2i2i2−i2i2−i2−i2i20000000000000000
χ392222-2-2-2-2-2-2222000-2-202−2−2−2−22222-2200000022−2−222−2−2−2−22200002i−2i−2i2i−i2i2i2−i2i2−i2−i2i20000000000000000
χ402222-2-2-2-2-2-2222000-2-202−2−2−2−22222-2200000022−2−222−2−2−2−2220000−2i2i2i−2ii2−i2−i2i2−i2i2i2−i20000000000000000
χ412222-2-2-2-2-2-22-2-200022022222−2−2−2−22-200000022−2−2−2−222−2−2222-2-2200002−22−2−22−220000000000000000
χ422222-2-2-2-2-2-22-2-200022022222−2−2−2−22-200000022−2−2−2−222−2−222-222-20000−22−222−22−20000000000000000
χ432222-2-2-2-2-2-22-2-20002202−2−2−2−222222-2000000−2−22222−2−222−2−22-2-220000−22−222−22−20000000000000000
χ442222-2-2-2-2-2-22-2-20002202−2−2−2−222222-2000000−2−22222−2−222−2−2-222-200002−22−2−22−220000000000000000
χ4522-2-22-2-220002-222-22-2-202i2i−2i−2i2i2i−2i−2i0000002-2000000002i−2i2i−2i0000000000000000000000002−22−2i2−i2i2−i2
χ4622-2-22-2-220002-222-22-2-202i2i−2i−2i2i2i−2i−2i0000002-2000000002i−2i2i−2i000000000000000000000000−22−22−i2i2−i2i2
χ4722-2-22-2-220002-222-22-2-20−2i−2i2i2i−2i−2i2i2i0000002-200000000−2i2i−2i2i0000000000000000000000002−22−2−i2i2−i2i2
χ4822-2-22-2-220002-222-22-2-20−2i−2i2i2i−2i−2i2i2i0000002-200000000−2i2i−2i2i000000000000000000000000−22−22i2−i2i2−i2
χ4922-2-22-2-22000-2222-2-22-202i2i−2i−2i2i2i−2i−2i000000-2200000000−2i2i−2i2i000000000000000000000000i2−i2−i2i2−222−2
χ5022-2-22-2-22000-2222-2-22-202i2i−2i−2i2i2i−2i−2i000000-2200000000−2i2i−2i2i000000000000000000000000−i2i2i2−i22−2−22
χ5122-2-22-2-22000-2222-2-22-20−2i−2i2i2i−2i−2i2i2i000000-22000000002i−2i2i−2i000000000000000000000000i2−i2−i2i22−2−22
χ5222-2-22-2-22000-2222-2-22-20−2i−2i2i2i−2i−2i2i2i000000-22000000002i−2i2i−2i000000000000000000000000−i2i2i2−i2−222−2
χ532-22-2-22-222-22002-2-2002-22-22-22-22-200002-20000002-22-200000000000000000000i2−i2i2−i2i2−i2i2−i200000000
χ542-22-2-22-222-22002-2-2002-22-22-22-22-200002-20000002-22-200000000000000000000−i2i2−i2i2−i2i2−i2i200000000
χ552-22-2-22-222-22002-2-2002-2-22-22-22-2200002-2000000-22-2200000000000000000000i2−i2i2−i2−i2i2−i2i200000000
χ562-22-2-22-222-22002-2-2002-2-22-22-22-2200002-2000000-22-2200000000000000000000−i2i2−i2i2i2−i2i2−i200000000
χ572-22-2-22-22-22-2002-2-200222-22-22-22-20000-22000000-22-22000000000000000000002−2−222−2−2200000000
χ582-22-2-22-22-22-2002-2-200222-22-22-22-20000-22000000-22-2200000000000000000000−222−2−222−200000000
χ592-22-2-22-22-22-2002-2-20022-22-22-22-220000-220000002-22-2000000000000000000002−2−22−222−200000000
χ602-22-2-22-22-22-2002-2-20022-22-22-22-220000-220000002-22-200000000000000000000−222−22−2−2200000000
χ6144-4-44-4-440004-4-4-444-44000000000000000-4400000000000000000000000000000000000000000000
χ6244-4-44-4-44000-44-4-44-4440000000000000004-400000000000000000000000000000000000000000000
χ6344-4-4-444-40004-4000-44002i22i2−2i2−2i2−2i2−2i22i22i200000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ6444-4-4-444-40004-4000-4400−2i2−2i22i22i22i22i2−2i2−2i20000000000000000−2i22i22i2−2i200000000000000000000000000000000
χ6544-4-4-444-4000-440004-4002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000−2i22i22i2−2i200000000000000000000000000000000
χ6644-4-4-444-4000-440004-400−2i2−2i22i22i22i22i2−2i2−2i200000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ674-44-44-44-44-4-400000000422−2222−22−2222−222200000000000022−22−2222000000000000000000000000000000000000
χ684-44-44-44-44-4-4000000004−2222−222222−2222−22000000000000−222222−22000000000000000000000000000000000000
χ694-44-44-44-4-44400000000-422−2222−22−2222−2222000000000000−222222−22000000000000000000000000000000000000
χ704-44-44-44-4-44400000000-4−2222−222222−2222−2200000000000022−22−2222000000000000000000000000000000000000
χ714-44-4-44-444-4400-44400-4-4000000000000-440000000000000000000000000000000000000000000000
χ724-44-4-44-44-44-400-44400-440000000000004-40000000000000000000000000000000000000000000000
χ734-4-4444-4-40000000000002i2−2i2−2i22i2−2i22i22i2−2i2004i−4i000022−2222−220000000000000000000000000000000000000000
χ744-4-4444-4-40000000000002i2−2i2−2i22i2−2i22i22i2−2i200−4i4i0000−2222−22220000000000000000000000000000000000000000
χ754-4-4444-4-4000000000000−2i22i22i2−2i22i2−2i2−2i22i2004i−4i0000−2222−22220000000000000000000000000000000000000000
χ764-4-4444-4-4000000000000−2i22i22i2−2i22i2−2i2−2i22i200−4i4i000022−2222−220000000000000000000000000000000000000000
χ774-4-44-4-444000004-4400-404i−4i−4i4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ784-4-44-4-444000004-4400-40−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ794-4-44-4-44400000-44-4004000000000000000004-4-440000000000000000000000000000000000000000
χ804-4-44-4-44400000-44-400400000000000000000-444-40000000000000000000000000000000000000000

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