Finite Group Databasebeta

← Group #313681

Character table — Group #313681

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888822224488888888888888888888444444444488888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1
χ6111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111
χ7111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11-1-1-1-11-1-1-1-111
χ8111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-11111-11111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-111-1-1111-1-1-11
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11-1-111-1-1-1111-1
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1-1-1-111-1-11-1-1111-1
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-11-1-111-111-1-1-11
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-111111-1-11-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111111-1-1-1-1-111-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1111-1-111-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-11111111-1-1-111-1-11-1
χ17222222222-22-22-22-2000000002222-2-200002222-2-2-2-2000000002200-2-200-2-200000000000000000000
χ18222222222-22-22-22-2000000002222-2-20000-2-2-2-2222200000000-2-2002200-2-200000000000000000000
χ19222222222-22-22-22-200000000-2-2-2-2-2-200002222-2-2-2-200000000-2-20022002200000000000000000000
χ20222222222-22-22-22-200000000-2-2-2-2-2-20000-2-2-2-22222000000002200-2-2002200000000000000000000
χ2122222222-22-22-22-22222222220000-2-2-2-2-2-20000000000000000002200220000000000-20000-2000000
χ2222222222-22-22-22-22222222220000-2-2-2-2-2-2000000000000000000-2-200-2-20000000000200002000000
χ2322222222-22-22-22-22-2-2-2-2-2-2-2-20000-2-222220000000000000000002200-2-2000000000020000-2000000
χ2422222222-22-22-22-22-2-2-2-2-2-2-2-20000-2-22222000000000000000000-2-200220000000000-200002000000
χ252222-2-2-2-22020-20-202222−2−2−2−222-2-20022−2−222-2-200002222−2−2−2−22-20000000022−2−222−2−2000000000000
χ262222-2-2-2-22020-20-202222−2−2−2−222-2-20022−2−2-2-2220000−2−2−2−22222-2200000000−2−22222−2−2000000000000
χ272222-2-2-2-22020-20-202222−2−2−2−2-2-2220022−2−222-2-200002222−2−2−2−2-2200000000−2−222−2−222000000000000
χ282222-2-2-2-22020-20-202222−2−2−2−2-2-2220022−2−2-2-2220000−2−2−2−222222-20000000022−2−2−2−222000000000000
χ292222-2-2-2-22020-20-20−2−2−2−2222222-2-200−2−22222-2-20000−2−2−2−222222-200000000−2−222−2−222000000000000
χ302222-2-2-2-22020-20-20−2−2−2−2222222-2-200−2−222-2-22200002222−2−2−2−2-220000000022−2−2−2−222000000000000
χ312222-2-2-2-22020-20-20−2−2−2−22222-2-22200−2−22222-2-20000−2−2−2−22222-220000000022−2−222−2−2000000000000
χ322222-2-2-2-22020-20-20−2−2−2−22222-2-22200−2−222-2-22200002222−2−2−2−22-200000000−2−22222−2−2000000000000
χ3322-2-22-2-22020-20-20222-2-222-2-20000000000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2002i−2i002i−2i00000000000000002−22−200
χ3422-2-22-2-22020-20-20222-2-222-2-20000000000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200−2i2i00−2i2i0000000000000000−22−2200
χ3522-2-22-2-22020-20-20222-2-222-2-20000000000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2002i−2i002i−2i0000000000000000−22−2200
χ3622-2-22-2-22020-20-20222-2-222-2-20000000000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200−2i2i00−2i2i00000000000000002−22−200
χ3722-2-22-2-22020-20-202-2-222-2-2220000000000i2−i2i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2002i−2i00−2i2i00000000000000002−2−2200
χ3822-2-22-2-22020-20-202-2-222-2-2220000000000i2−i2i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200−2i2i002i−2i0000000000000000−222−200
χ3922-2-22-2-22020-20-202-2-222-2-2220000000000−i2i2−i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2002i−2i00−2i2i0000000000000000−222−200
χ4022-2-22-2-22020-20-202-2-222-2-2220000000000−i2i2−i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200−2i2i002i−2i00000000000000002−2−2200
χ412-22-22-22-220-20-2020i2−i2i2−i2i2−i2i2−i22-22-200i2−i2i2−i200002-22-2i2−i2i2−i2i2−i2i2−i200002-20000i2−i2i2−i2i2−i2i2−i2000000000000
χ422-22-22-22-220-20-2020i2−i2i2−i2i2−i2i2−i22-22-200i2−i2i2−i20000-22-22−i2i2−i2i2−i2i2−i2i20000-220000−i2i2−i2i2i2−i2i2−i2000000000000
χ432-22-22-22-220-20-2020i2−i2i2−i2i2−i2i2−i2-22-2200i2−i2i2−i200002-22-2i2−i2i2−i2i2−i2i2−i20000-220000−i2i2−i2i2−i2i2−i2i2000000000000
χ442-22-22-22-220-20-2020i2−i2i2−i2i2−i2i2−i2-22-2200i2−i2i2−i20000-22-22−i2i2−i2i2−i2i2−i2i200002-20000i2−i2i2−i2−i2i2−i2i2000000000000
χ452-22-22-22-220-20-2020−i2i2−i2i2−i2i2−i2i22-22-200−i2i2−i2i200002-22-2−i2i2−i2i2−i2i2−i2i200002-20000−i2i2−i2i2−i2i2−i2i2000000000000
χ462-22-22-22-220-20-2020−i2i2−i2i2−i2i2−i2i22-22-200−i2i2−i2i20000-22-22i2−i2i2−i2i2−i2i2−i20000-220000i2−i2i2−i2−i2i2−i2i2000000000000
χ472-22-22-22-220-20-2020−i2i2−i2i2−i2i2−i2i2-22-2200−i2i2−i2i200002-22-2−i2i2−i2i2−i2i2−i2i20000-220000i2−i2i2−i2i2−i2i2−i2000000000000
χ482-22-22-22-220-20-2020−i2i2−i2i2−i2i2−i2i2-22-2200−i2i2−i2i20000-22-22i2−i2i2−i2i2−i2i2−i200002-20000−i2i2−i2i2i2−i2i2−i2000000000000
χ492-22-2-22-2222-2-222-2-22i−2i2i−2i−2i2i−2i2i2-2-22-222i−2i−2i2i0000000000000000000000002-200002i−2i−2i2i000000000000
χ502-22-2-22-2222-2-222-2-22i−2i2i−2i−2i2i−2i2i-222-2-222i−2i−2i2i000000000000000000000000-220000−2i2i2i−2i000000000000
χ512-22-2-22-2222-2-222-2-2−2i2i−2i2i2i−2i2i−2i2-2-22-22−2i2i2i−2i0000000000000000000000002-20000−2i2i2i−2i000000000000
χ522-22-2-22-2222-2-222-2-2−2i2i−2i2i2i−2i2i−2i-222-2-22−2i2i2i−2i000000000000000000000000-2200002i−2i−2i2i000000000000
χ532-22-2-22-222-2-222-2-22000000002-2-222-20000000000002i−2i2i−2i−2i2i−2i2i00000000-222i−2i−2i2i0000000000000000
χ542-22-2-22-222-2-222-2-22000000002-2-222-2000000000000−2i2i−2i2i2i−2i2i−2i00000000-22−2i2i2i−2i0000000000000000
χ552-22-2-22-222-2-222-2-2200000000-222-22-20000000000002i−2i2i−2i−2i2i−2i2i000000002-2−2i2i2i−2i0000000000000000
χ562-22-2-22-222-2-222-2-2200000000-222-22-2000000000000−2i2i−2i2i2i−2i2i−2i000000002-22i−2i−2i2i0000000000000000
χ572-22-2-22-22-222-2-222-22i−2i2i−2i−2i2i−2i2i00002-2−2i2i2i−2i000000000000000000000000000000000002-22i−2i0000000
χ582-22-2-22-22-222-2-222-22i−2i2i−2i−2i2i−2i2i00002-2−2i2i2i−2i00000000000000000000000000000000000-22−2i2i0000000
χ592-22-2-22-22-222-2-222-2−2i2i−2i2i2i−2i2i−2i00002-22i−2i−2i2i000000000000000000000000000000000002-2−2i2i0000000
χ602-22-2-22-22-222-2-222-2−2i2i−2i2i2i−2i2i−2i00002-22i−2i−2i2i00000000000000000000000000000000000-222i−2i0000000
χ6144444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-40-40404022222222−22−22−22−22000000−22−2222220000000000000000000000000000000000000000000000
χ634444-4-4-4-4-40-404040−22−22−22−22222222220000002222−22−220000000000000000000000000000000000000000000000
χ6444-4-44-4-440-404040-40000000000000000002i2−2i22i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ6544-4-44-4-440-404040-4000000000000000000−2i22i2−2i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ6644-4-4-444-4000000002222−22−22−22−22222200000000002i2−2i2−2i22i200002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ6744-4-4-444-4000000002222−22−22−22−2222220000000000−2i22i22i2−2i20000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6844-4-4-444-400000000−22−2222222222−22−2200000000002i2−2i2−2i22i20000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ6944-4-4-444-400000000−22−2222222222−22−220000000000−2i22i22i2−2i200002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ704-44-44-44-4-404040-402i2−2i22i2−2i22i2−2i22i2−2i2000000−2i22i2−2i22i20000000000000000000000000000000000000000000000
χ714-44-44-44-4-404040-40−2i22i2−2i22i2−2i22i2−2i22i20000002i2−2i22i2−2i20000000000000000000000000000000000000000000000
χ724-44-4-44-44-4-444-4-444000000000000-4400000000000000000000000000000000000000000000000000
χ734-4-4444-4-4000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000002i2−2i2−2i22i2-222-2-222-2000000000000000000000000000000
χ744-4-4444-4-4000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000−2i22i22i2−2i22-2-222-2-22000000000000000000000000000000
χ754-4-4444-4-400000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000002i2−2i2−2i22i22-2-222-2-22000000000000000000000000000000
χ764-4-4444-4-400000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000−2i22i22i2−2i2-222-2-222-2000000000000000000000000000000
χ774-4-44-4-44404040-40-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ784-4-44-4-44404040-40-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ794-4-44-4-4440-40-404040000000000000000000000000022−22−2222−222222−22000000000000000000000000000000
χ804-4-44-4-4440-40-4040400000000000000000000000000−222222−2222−22−2222000000000000000000000000000000

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