Finite Group Databasebeta

← Group #98985

Character table — Group #98985

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
χ91111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ121111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ131111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222-2-2-2-22222222222-2-2-2-222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ1822222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-2222200000000000000000000000000000000
χ192222222222-2-2-2-222222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ202222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
χ2122222222-2-222222222-2-20000000022-2-2-2-2-2-200000000000022-2-222-2-2000000000000000000000000
χ2222222222-2-222222222-2-20000000022-2-2-2-2-2-2000000000000-2-222-2-222000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-200000000-2-222-2-222000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2422222222-2-22222-2-2-2-2-2-200000000-2-222-2-22200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2522222222-2-2-2-2-2-22222-2-200000000-2-22222-2-2000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2622222222-2-2-2-2-2-22222-2-200000000-2-22222-2-200000000000000000000−2i−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
χ2922-2-222-2-20022-2-222-2-200i2i2i2i2−i2−i2−i2−i22-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002i−2i002i−2i2−22−22−22−20000000000000000
χ3022-2-222-2-20022-2-222-2-200i2i2i2i2−i2−i2−i2−i22-2000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200−2i2i00−2i2i−22−22−22−220000000000000000
χ3122-2-222-2-20022-2-222-2-200−i2−i2−i2−i2i2i2i2i22-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002i−2i002i−2i−22−22−22−220000000000000000
χ3222-2-222-2-20022-2-222-2-200−i2−i2−i2−i2i2i2i2i22-2000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200−2i2i00−2i2i2−22−22−22−20000000000000000
χ3322-2-222-2-20022-2-2-2-22200i2i2i2i2−i2−i2−i2−i2-22000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i22-2002-200i2−i2−i2i2i2−i2−i2i20000000000000000
χ3422-2-222-2-20022-2-2-2-22200i2i2i2i2−i2−i2−i2−i2-22000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2-2200-2200−i2i2i2−i2−i2i2i2−i20000000000000000
χ3522-2-222-2-20022-2-2-2-22200−i2−i2−i2−i2i2i2i2i2-22000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i22-2002-200−i2i2i2−i2−i2i2i2−i20000000000000000
χ3622-2-222-2-20022-2-2-2-22200−i2−i2−i2−i2i2i2i2i2-22000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2-2200-2200i2−i2−i2i2i2−i2−i2i20000000000000000
χ3722-2-222-2-200-2-22222-2-200i2i2i2i2−i2−i2−i2−i2-22000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i22-200-2200i2−i2−i2i2−i2i2i2−i20000000000000000
χ3822-2-222-2-200-2-22222-2-200i2i2i2i2−i2−i2−i2−i2-22000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2-22002-200−i2i2i2−i2i2−i2−i2i20000000000000000
χ3922-2-222-2-200-2-22222-2-200−i2−i2−i2−i2i2i2i2i2-22000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i22-200-2200−i2i2i2−i2i2−i2−i2i20000000000000000
χ4022-2-222-2-200-2-22222-2-200−i2−i2−i2−i2i2i2i2i2-22000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2-22002-200i2−i2−i2i2−i2i2i2−i20000000000000000
χ4122-2-222-2-200-2-222-2-22200i2i2i2i2−i2−i2−i2−i22-2000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2002i−2i00−2i2i2−22−2−22−220000000000000000
χ4222-2-222-2-200-2-222-2-22200i2i2i2i2−i2−i2−i2−i22-2000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200−2i2i002i−2i−22−222−22−20000000000000000
χ4322-2-222-2-200-2-222-2-22200−i2−i2−i2−i2i2i2i2i22-2000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2002i−2i00−2i2i−22−222−22−20000000000000000
χ4422-2-222-2-200-2-222-2-22200−i2−i2−i2−i2i2i2i2i22-2000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200−2i2i002i−2i2−22−2−22−220000000000000000
χ452-22-22-22-22-200002i−2i2i−2i2-222-2-222-2-20000002i−2i000000002i−2i2i−2i00000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ462-22-22-22-22-200002i−2i2i−2i2-222-2-222-2-20000002i−2i000000002i−2i2i−2i0000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ472-22-22-22-22-200002i−2i2i−2i2-2-2-222-2-2220000002i−2i00000000−2i2i−2i2i00000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ482-22-22-22-22-200002i−2i2i−2i2-2-2-222-2-2220000002i−2i00000000−2i2i−2i2i0000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ492-22-22-22-22-20000−2i2i−2i2i2-222-2-222-2-2000000−2i2i00000000−2i2i−2i2i00000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ502-22-22-22-22-20000−2i2i−2i2i2-222-2-222-2-2000000−2i2i00000000−2i2i−2i2i0000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ512-22-22-22-22-20000−2i2i−2i2i2-2-2-222-2-222000000−2i2i000000002i−2i2i−2i00000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ522-22-22-22-22-20000−2i2i−2i2i2-2-2-222-2-222000000−2i2i000000002i−2i2i−2i0000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ532-22-2-22-222-22i−2i2i−2i0000-222-22-22-22-200002i−2i0000002i−2i2i−2i00000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ542-22-2-22-222-22i−2i2i−2i0000-222-22-22-22-200002i−2i0000002i−2i2i−2i0000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ552-22-2-22-222-22i−2i2i−2i0000-22-22-22-22-2200002i−2i000000−2i2i−2i2i00000000000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i
χ562-22-2-22-222-22i−2i2i−2i0000-22-22-22-22-2200002i−2i000000−2i2i−2i2i0000000000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i
χ572-22-2-22-222-2−2i2i−2i2i0000-222-22-22-22-20000−2i2i000000−2i2i−2i2i00000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ582-22-2-22-222-2−2i2i−2i2i0000-222-22-22-22-20000−2i2i000000−2i2i−2i2i0000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ592-22-2-22-222-2−2i2i−2i2i0000-22-22-22-22-220000−2i2i0000002i−2i2i−2i00000000000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i
χ602-22-2-22-222-2−2i2i−2i2i0000-22-22-22-22-220000−2i2i0000002i−2i2i−2i0000000000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i
χ614444-4-4-4-44400000000-4-44-4-444-4-440000000000000000000000000000000000000000000000000000
χ624444-4-4-4-44400000000-4-4-444-4-444-40000000000000000000000000000000000000000000000000000
χ634444-4-4-4-4-4-4000000004400000000000000004i−4i4i−4i0000000000000000000000000000000000000000
χ644444-4-4-4-4-4-400000000440000000000000000−4i4i−4i4i0000000000000000000000000000000000000000
χ6544-4-4-4-4440000000000002i2−2i2−2i22i2−2i22i22i2−2i2004i−4i000022−22−22220000000000000000000000000000000000000000
χ6644-4-4-4-4440000000000002i2−2i2−2i22i2−2i22i22i2−2i200−4i4i0000−222222−220000000000000000000000000000000000000000
χ6744-4-4-4-444000000000000−2i22i22i2−2i22i2−2i2−2i22i2004i−4i0000−222222−220000000000000000000000000000000000000000
χ6844-4-4-4-444000000000000−2i22i22i2−2i22i2−2i2−2i22i200−4i4i000022−22−22220000000000000000000000000000000000000000
χ694-44-44-44-4-4400004i−4i4i−4i-4400000000000000−4i4i00000000000000000000000000000000000000000000
χ704-44-44-44-4-440000−4i4i−4i4i-44000000000000004i−4i00000000000000000000000000000000000000000000
χ714-44-4-44-44-444i−4i4i−4i00004-4000000000000−4i4i0000000000000000000000000000000000000000000000
χ724-44-4-44-44-44−4i4i−4i4i00004-40000000000004i−4i0000000000000000000000000000000000000000000000
χ734-4-444-4-440000004i−4i−4i4i002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000−222222−2200000000000000000000000000000000
χ744-4-444-4-440000004i−4i−4i4i00−2i2−2i22i22i22i22i2−2i2−2i2000000000000000022−22−222200000000000000000000000000000000
χ754-4-444-4-44000000−4i4i4i−4i002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000022−22−222200000000000000000000000000000000
χ764-4-444-4-44000000−4i4i4i−4i00−2i2−2i22i22i22i22i2−2i2−2i20000000000000000−222222−2200000000000000000000000000000000
χ774-4-44-444-4004i−4i−4i4i0000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000−222222−22000000000000000000000000000000000000
χ784-4-44-444-4004i−4i−4i4i000000−2i22i2−2i22i22i2−2i22i2−2i200000000000022−22−2222000000000000000000000000000000000000
χ794-4-44-444-400−4i4i4i−4i0000002i2−2i22i2−2i2−2i22i2−2i22i200000000000022−22−2222000000000000000000000000000000000000
χ804-4-44-444-400−4i4i4i−4i000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000−222222−22000000000000000000000000000000000000

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