Finite Group Databasebeta

← Group #313621

Character table — Group #313621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888822224488888888888888888888444444444488888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-11
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11-1-1-11111-1-11-1
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1-1-1111-1-111-1-11-1
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-11-1-1-111-1-111-11
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-11-1-111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-111-1-111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-11-1-11111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111111-111-1-1-1-1111-1
χ17222222222-22-22-22-2000000002222-2-200002222-2-2-2-20000000022-2-200-2-20000000000000000000000
χ18222222222-22-22-22-2000000002222-2-20000-2-2-2-2222200000000-2-22200-2-20000000000000000000000
χ19222222222-22-22-22-200000000-2-2-2-2-2-200002222-2-2-2-200000000-2-22200220000000000000000000000
χ20222222222-22-22-22-200000000-2-2-2-2-2-20000-2-2-2-222220000000022-2-200220000000000000000000000
χ2122222222-22-22-22-22222222220000-2-2-2-2-2-20000000000000000000022002200000000-2-20000000000
χ2222222222-22-22-22-22222222220000-2-2-2-2-2-200000000000000000000-2-200-2-200000000220000000000
χ2322222222-22-22-22-22-2-2-2-2-2-2-2-20000-2-22222000000000000000000002200-2-2000000002-20000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2-2-20000-2-2222200000000000000000000-2-2002200000000-220000000000
χ2522-2-222-2-2-20-2020202222−2−2−2−222-2-20022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i22i−2i00000000i2i2−i2−i222−2−2000000000000
χ2622-2-222-2-2-20-2020202222−2−2−2−222-2-20022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i2−2i2i00000000−i2−i2i2i222−2−2000000000000
χ2722-2-222-2-2-20-2020202222−2−2−2−2-2-2220022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i2−2i2i00000000−i2−i2i2i2−2−222000000000000
χ2822-2-222-2-2-20-2020202222−2−2−2−2-2-2220022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i22i−2i00000000i2i2−i2−i2−2−222000000000000
χ2922-2-222-2-2-20-202020−2−2−2−2222222-2-200−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i22i−2i00000000−i2−i2i2i2−2−222000000000000
χ3022-2-222-2-2-20-202020−2−2−2−2222222-2-200−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i2−2i2i00000000i2i2−i2−i2−2−222000000000000
χ3122-2-222-2-2-20-202020−2−2−2−22222-2-22200−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i2−2i2i00000000i2i2−i2−i222−2−2000000000000
χ3222-2-222-2-2-20-202020−2−2−2−22222-2-22200−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i22i−2i00000000−i2−i2i2i222−2−2000000000000
χ3322-2-2-2-222020-20-20222-2-222-2-20000000000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200002-2002-200000000000000i2−i2i2−i200
χ3422-2-2-2-222020-20-20222-2-222-2-20000000000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000-2200-2200000000000000−i2i2−i2i200
χ3522-2-2-2-222020-20-20222-2-222-2-20000000000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200002-2002-200000000000000−i2i2−i2i200
χ3622-2-2-2-222020-20-20222-2-222-2-20000000000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000-2200-2200000000000000i2−i2i2−i200
χ3722-2-2-2-222020-20-202-2-222-2-2220000000000i2−i2i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200002-200-2200000000000000−i2i2i2−i200
χ3822-2-2-2-222020-20-202-2-222-2-2220000000000i2−i2i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000-22002-200000000000000i2−i2−i2i200
χ3922-2-2-2-222020-20-202-2-222-2-2220000000000−i2i2−i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200002-200-2200000000000000i2−i2−i2i200
χ4022-2-2-2-222020-20-202-2-222-2-2220000000000−i2i2−i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000-22002-200000000000000−i2i2i2−i200
χ412-22-22-2-2222-2-222-2-22i−2i2i−2i2i−2i2i−2i2-22-2-222i−2i2i−2i00000000000000000000002-20000002i−2i2i−2i000000000000
χ422-22-22-2-2222-2-222-2-22i−2i2i−2i2i−2i2i−2i-22-22-222i−2i2i−2i0000000000000000000000-22000000−2i2i−2i2i000000000000
χ432-22-22-2-2222-2-222-2-2−2i2i−2i2i−2i2i−2i2i2-22-2-22−2i2i−2i2i00000000000000000000002-2000000−2i2i−2i2i000000000000
χ442-22-22-2-2222-2-222-2-2−2i2i−2i2i−2i2i−2i2i-22-22-22−2i2i−2i2i0000000000000000000000-220000002i−2i2i−2i000000000000
χ452-22-22-2-222-2-222-2-22000000002-22-22-20000000000002i−2i2i−2i2i−2i2i−2i000000-22002i−2i2i−2i0000000000000000
χ462-22-22-2-222-2-222-2-22000000002-22-22-2000000000000−2i2i−2i2i−2i2i−2i2i000000-2200−2i2i−2i2i0000000000000000
χ472-22-22-2-222-2-222-2-2200000000-22-222-20000000000002i−2i2i−2i2i−2i2i−2i0000002-200−2i2i−2i2i0000000000000000
χ482-22-22-2-222-2-222-2-2200000000-22-222-2000000000000−2i2i−2i2i−2i2i−2i2i0000002-2002i−2i2i−2i0000000000000000
χ492-22-22-2-22-222-2-222-22i−2i2i−2i2i−2i2i−2i00002-2−2i2i−2i2i0000000000000000000000000000000000002i−2i2-2000000
χ502-22-22-2-22-222-2-222-22i−2i2i−2i2i−2i2i−2i00002-2−2i2i−2i2i000000000000000000000000000000000000−2i2i-22000000
χ512-22-22-2-22-222-2-222-2−2i2i−2i2i−2i2i−2i2i00002-22i−2i2i−2i0000000000000000000000000000000000002i−2i-22000000
χ522-22-22-2-22-222-2-222-2−2i2i−2i2i−2i2i−2i2i00002-22i−2i2i−2i000000000000000000000000000000000000−2i2i2-2000000
χ532-2-222-22-2-202020-20i2−i2i2−i2−i2i2−i2i22-2-2200i2−i2−i2i200002i−2i2i−2i2−22−2−22−22002i−2i0000002−2−22i2−i2−i2i2000000000000
χ542-2-222-22-2-202020-20i2−i2i2−i2−i2i2−i2i22-2-2200i2−i2−i2i20000−2i2i−2i2i−22−222−22−200−2i2i000000−222−2i2−i2−i2i2000000000000
χ552-2-222-22-2-202020-20i2−i2i2−i2−i2i2−i2i2-222-200i2−i2−i2i200002i−2i2i−2i2−22−2−22−2200−2i2i000000−222−2−i2i2i2−i2000000000000
χ562-2-222-22-2-202020-20i2−i2i2−i2−i2i2−i2i2-222-200i2−i2−i2i20000−2i2i−2i2i−22−222−22−2002i−2i0000002−2−22−i2i2i2−i2000000000000
χ572-2-222-22-2-202020-20−i2i2−i2i2i2−i2i2−i22-2-2200−i2i2i2−i200002i−2i2i−2i−22−222−22−2002i−2i000000−222−2−i2i2i2−i2000000000000
χ582-2-222-22-2-202020-20−i2i2−i2i2i2−i2i2−i22-2-2200−i2i2i2−i20000−2i2i−2i2i2−22−2−22−2200−2i2i0000002−2−22−i2i2i2−i2000000000000
χ592-2-222-22-2-202020-20−i2i2−i2i2i2−i2i2−i2-222-200−i2i2i2−i200002i−2i2i−2i−22−222−22−200−2i2i0000002−2−22i2−i2−i2i2000000000000
χ602-2-222-22-2-202020-20−i2i2−i2i2i2−i2i2−i2-222-200−i2i2i2−i20000−2i2i−2i2i2−22−2−22−22002i−2i000000−222−2i2−i2−i2i2000000000000
χ6144444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ624444-4-4-4-4000000002222−22−22−22−222222000000000022−22−2222000022-2-2-2-222000000000000000000000000000000
χ634444-4-4-4-4000000002222−22−22−22−2222220000000000−222222−220000-2-22222-2-2000000000000000000000000000000
χ644444-4-4-4-400000000−22−2222222222−22−22000000000022−22−22220000-2-22222-2-2000000000000000000000000000000
χ654444-4-4-4-400000000−22−2222222222−22−220000000000−222222−22000022-2-2-2-222000000000000000000000000000000
χ6644-4-444-4-44040-40-4022222222−22−22−22−22000000−22−2222220000000000000000000000000000000000000000000000
χ6744-4-444-4-44040-40-40−22−22−22−22222222220000002222−22−220000000000000000000000000000000000000000000000
χ6844-4-4-4-4440-404040-40000000000000000002i2−2i22i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ6944-4-4-4-4440-404040-4000000000000000000−2i22i2−2i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ704-44-44-4-44-4-444-4-444000000000000-4400000000000000000000000000000000000000000000000000
χ714-44-4-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000022−22−2222−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ724-44-4-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000−222222−222i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ734-44-4-444-400000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000022−22−22222i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ744-44-4-444-400000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000−222222−22−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ754-4-444-44-440-40-40402i2−2i22i2−2i2−2i22i2−2i22i2000000−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ764-4-444-44-440-40-4040−2i22i2−2i22i22i2−2i22i2−2i20000002i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ774-4-44-44-4404040-40-44i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ784-4-44-44-4404040-40-4−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ794-4-44-44-440-40-404040000000000000000000000000022−22−222222−22−2222000000000000000000000000000000
χ804-4-44-44-440-40-4040400000000000000000000000000−222222−22−222222−22000000000000000000000000000000

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