Finite Group Databasebeta

← Group #313698

Character table — Group #313698

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888444444444488888888224444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ61111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ71111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111-1-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-11
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111-11-1-111-1-11-1
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-1-1-1-1-11-11111-1-11-1
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1-1-111-11-1-1-1-111-11
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111111-1-1-1-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-111111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-11111111-1-1-111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-1-1-11111-1-1-1111-1-1111-1
χ17222222222-22-22-22-200000000-22222-222220000-2-2-2-200000000-2-2-2-222000000000000000000000000
χ18222222222-22-22-22-200000000-22222-2-2-2-2-2000022220000000022-2-2-2-2000000000000000000000000
χ19222222222-22-22-22-200000000-2-2-2-2-2-222220000-2-2-2-2000000002222-2-2000000000000000000000000
χ20222222222-22-22-22-200000000-2-2-2-2-2-2-2-2-2-20000222200000000-2-22222000000000000000000000000
χ2122222222-22-22-22-2222222222-20000-20000-2-2-2-200000000000000000022220000000000-2-200000000
χ2222222222-22-22-22-2222222222-20000-20000-2-2-2-2000000000000000000-2-2-2-200000000002200000000
χ2322222222-22-22-22-22-2-2-2-2-2-2-2-2-20000-20000222200000000000000000022-2-20000000000-2200000000
χ2422222222-22-22-22-22-2-2-2-2-2-2-2-2-20000-200002222000000000000000000-2-22200000000002-200000000
χ2522-22-22-2-220-20-2020i2i2i2i2−i2−i2−i2−i202i2i−2i−2i00000i2i2−i2−i222-2-2i2i2i2i2−i2−i2−i2−i22i−2i0000000022−2−222−2−2000000000000
χ2622-22-22-2-220-20-2020i2i2i2i2−i2−i2−i2−i202i2i−2i−2i00000i2i2−i2−i2-2-222−i2−i2−i2−i2i2i2i2i2−2i2i00000000−2−22222−2−2000000000000
χ2722-22-22-2-220-20-2020i2i2i2i2−i2−i2−i2−i20−2i−2i2i2i00000i2i2−i2−i222-2-2i2i2i2i2−i2−i2−i2−i2−2i2i00000000−2−222−2−222000000000000
χ2822-22-22-2-220-20-2020i2i2i2i2−i2−i2−i2−i20−2i−2i2i2i00000i2i2−i2−i2-2-222−i2−i2−i2−i2i2i2i2i22i−2i0000000022−2−2−2−222000000000000
χ2922-22-22-2-220-20-2020−i2−i2−i2−i2i2i2i2i202i2i−2i−2i00000−i2−i2i2i222-2-2−i2−i2−i2−i2i2i2i2i22i−2i00000000−2−222−2−222000000000000
χ3022-22-22-2-220-20-2020−i2−i2−i2−i2i2i2i2i202i2i−2i−2i00000−i2−i2i2i2-2-222i2i2i2i2−i2−i2−i2−i2−2i2i0000000022−2−2−2−222000000000000
χ3122-22-22-2-220-20-2020−i2−i2−i2−i2i2i2i2i20−2i−2i2i2i00000−i2−i2i2i222-2-2−i2−i2−i2−i2i2i2i2i2−2i2i0000000022−2−222−2−2000000000000
χ3222-22-22-2-220-20-2020−i2−i2−i2−i2i2i2i2i20−2i−2i2i2i00000−i2−i2i2i2-2-222i2i2i2i2−i2−i2−i2−i22i−2i00000000−2−22222−2−2000000000000
χ3322-2-22-2-2202020-20-222-2-222-2-200000022−2−200002−22−222−2−222−2−20000002i−2i2i−2i00000000000000i2−i2i2−i200
χ3422-2-22-2-2202020-20-222-2-222-2-200000022−2−200002−22−222−2−222−2−2000000−2i2i−2i2i00000000000000−i2i2−i2i200
χ3522-2-22-2-2202020-20-222-2-222-2-2000000−2−2220000−22−22−2−222−2−2220000002i−2i2i−2i00000000000000−i2i2−i2i200
χ3622-2-22-2-2202020-20-222-2-222-2-2000000−2−2220000−22−22−2−222−2−222000000−2i2i−2i2i00000000000000i2−i2i2−i200
χ3722-2-22-2-2202020-20-2-2-222-2-22200000022−2−200002−22−2−2−222−2−2220000002i−2i−2i2i00000000000000−i2i2i2−i200
χ3822-2-22-2-2202020-20-2-2-222-2-22200000022−2−200002−22−2−2−222−2−222000000−2i2i2i−2i00000000000000i2−i2−i2i200
χ3922-2-22-2-2202020-20-2-2-222-2-222000000−2−2220000−22−2222−2−222−2−20000002i−2i−2i2i00000000000000i2−i2−i2i200
χ4022-2-22-2-2202020-20-2-2-222-2-222000000−2−2220000−22−2222−2−222−2−2000000−2i2i2i−2i00000000000000−i2i2i2−i200
χ412-222-2-2-222020-20-202−22−22−22−202i−2i2i−2i02-22-22−22−200002−22−22−22−200002i−2i0000i2−i2i2−i2i2−i2i2−i2000000000000
χ422-222-2-2-222020-20-202−22−22−22−202i−2i2i−2i0-22-222−22−20000−22−22−22−220000−2i2i0000−i2i2−i2i2i2−i2i2−i2000000000000
χ432-222-2-2-222020-20-202−22−22−22−20−2i2i−2i2i02-22-22−22−200002−22−22−22−20000−2i2i0000−i2i2−i2i2−i2i2−i2i2000000000000
χ442-222-2-2-222020-20-202−22−22−22−20−2i2i−2i2i0-22-222−22−20000−22−22−22−2200002i−2i0000i2−i2i2−i2−i2i2−i2i2000000000000
χ452-222-2-2-222020-20-20−22−22−22−2202i−2i2i−2i02-22-2−22−220000−22−22−22−2200002i−2i0000−i2i2−i2i2−i2i2−i2i2000000000000
χ462-222-2-2-222020-20-20−22−22−22−2202i−2i2i−2i0-22-22−22−2200002−22−22−22−20000−2i2i0000i2−i2i2−i2−i2i2−i2i2000000000000
χ472-222-2-2-222020-20-20−22−22−22−220−2i2i−2i2i02-22-2−22−220000−22−22−22−220000−2i2i0000i2−i2i2−i2i2−i2i2−i2000000000000
χ482-222-2-2-222020-20-20−22−22−22−220−2i2i−2i2i0-22-22−22−2200002−22−22−22−200002i−2i0000−i2i2−i2i2i2−i2i2−i2000000000000
χ492-2-222-22-222-2-222-2-22i−2i2i−2i−2i2i−2i2i-22-2-22200002i−2i−2i2i000000000000002-20000000000−2i2i2i−2i000000000000
χ502-2-222-22-222-2-222-2-22i−2i2i−2i−2i2i−2i2i-2-222-2200002i−2i−2i2i00000000000000-2200000000002i−2i−2i2i000000000000
χ512-2-222-22-222-2-222-2-2−2i2i−2i2i2i−2i2i−2i-22-2-2220000−2i2i2i−2i000000000000002-200000000002i−2i−2i2i000000000000
χ522-2-222-22-222-2-222-2-2−2i2i−2i2i2i−2i2i−2i-2-222-220000−2i2i2i−2i00000000000000-220000000000−2i2i2i−2i000000000000
χ532-2-222-22-22-2-222-2-220000000022-2-22-20000000000002i−2i2i−2i−2i2i−2i2i00-22000000−2i2i2i−2i0000000000000000
χ542-2-222-22-22-2-222-2-220000000022-2-22-2000000000000−2i2i−2i2i2i−2i2i−2i00-220000002i−2i−2i2i0000000000000000
χ552-2-222-22-22-2-222-2-22000000002-222-2-20000000000002i−2i2i−2i−2i2i−2i2i002-20000002i−2i−2i2i0000000000000000
χ562-2-222-22-22-2-222-2-22000000002-222-2-2000000000000−2i2i−2i2i2i−2i2i−2i002-2000000−2i2i2i−2i0000000000000000
χ572-2-222-22-2-222-2-222-22i−2i2i−2i−2i2i−2i2i20000-20000−2i2i2i−2i0000000000000000000000000000002-2002i−2i000000
χ582-2-222-22-2-222-2-222-22i−2i2i−2i−2i2i−2i2i20000-20000−2i2i2i−2i000000000000000000000000000000-2200−2i2i000000
χ592-2-222-22-2-222-2-222-2−2i2i−2i2i2i−2i2i−2i20000-200002i−2i−2i2i0000000000000000000000000000002-200−2i2i000000
χ602-2-222-22-2-222-2-222-2−2i2i−2i2i2i−2i2i−2i20000-200002i−2i−2i2i000000000000000000000000000000-22002i−2i000000
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ62444-4-4-44-4000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000022−22−22222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ63444-4-4-44-4000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000−222222−22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ64444-4-4-44-400000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000022−22−2222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ65444-4-4-44-400000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000−222222−222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6644-44-44-4-4-404040-402i22i22i22i2−2i2−2i2−2i2−2i20000000000−2i2−2i22i22i2000000000000000000000000000000000000000000
χ6744-44-44-4-4-404040-40−2i2−2i2−2i2−2i22i22i22i22i200000000002i22i2−2i2−2i2000000000000000000000000000000000000000000
χ6844-4-44-4-440-40-40404000000000000002222−22−220000−2222−222200000000000000000000000000000000000000
χ6944-4-44-4-440-40-4040400000000000000−22−222222000022−2222−2200000000000000000000000000000000000000
χ704-444-4-4-44-40-40404022−2222−2222−2222−220000000000−2222−2222000000000000000000000000000000000000000000
χ714-444-4-4-44-40-404040−2222−2222−2222−2222000000000022−2222−22000000000000000000000000000000000000000000
χ724-44-444-4-4040-40-4044i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ734-44-444-4-4040-40-404−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ744-44-444-4-40-404040-4000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ754-44-444-4-40-404040-400000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ764-4-444-44-4-4-444-4-44400000000-40000400000000000000000000000000000000000000000000000000
χ774-4-4-4-44440000000022−22−222222−22−222200000022−22−2222000000002-2-222-2-22000000000000000000000000000000
χ784-4-4-4-44440000000022−22−222222−22−2222000000−222222−2200000000-222-2-222-2000000000000000000000000000000
χ794-4-4-4-444400000000−222222−22−222222−2200000022−22−222200000000-222-2-222-2000000000000000000000000000000
χ804-4-4-4-444400000000−222222−22−222222−22000000−222222−22000000002-2-222-2-22000000000000000000000000000000

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