Finite Group Databasebeta

← Group #313613

Character table — Group #313613

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888822224488888888888888888888444444444488888888444444888824
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
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-11
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-11-1
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1-11-111-1-111-1-11-1
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-11-1-111-1-111-11
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-1-111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1111-1-111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111-1-1-11111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1111-1-1-1-1111-1
χ17222222222-22-22-22-2000000002222-2-200002222-2-2-2-200000000-2-22200-2-20000000000000000000000
χ18222222222-22-22-22-2000000002222-2-20000-2-2-2-222220000000022-2-200-2-20000000000000000000000
χ19222222222-22-22-22-200000000-2-2-2-2-2-200002222-2-2-2-20000000022-2-200220000000000000000000000
χ20222222222-22-22-22-200000000-2-2-2-2-2-20000-2-2-2-2222200000000-2-22200220000000000000000000000
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
χ2322222222-22-22-22-22-2-2-2-2-2-2-2-20000-2-22222000000000000000000002200-2-200000000-220000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2-2-20000-2-2222200000000000000000000-2-20022000000002-20000000000
χ25222-2-22-2-2-20-2020202222−2−2−2−222-2-20022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i2002i−2i000000i2i2−i2−i222−2−2000000000000
χ26222-2-22-2-2-20-2020202222−2−2−2−222-2-20022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i200−2i2i000000−i2−i2i2i222−2−2000000000000
χ27222-2-22-2-2-20-2020202222−2−2−2−2-2-2220022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i200−2i2i000000−i2−i2i2i2−2−222000000000000
χ28222-2-22-2-2-20-2020202222−2−2−2−2-2-2220022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i2002i−2i000000i2i2−i2−i2−2−222000000000000
χ29222-2-22-2-2-20-202020−2−2−2−2222222-2-200−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i2002i−2i000000−i2−i2i2i2−2−222000000000000
χ30222-2-22-2-2-20-202020−2−2−2−2222222-2-200−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i200−2i2i000000i2i2−i2−i2−2−222000000000000
χ31222-2-22-2-2-20-202020−2−2−2−22222-2-22200−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i200−2i2i000000i2i2−i2−i222−2−2000000000000
χ32222-2-22-2-2-20-202020−2−2−2−22222-2-22200−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i2002i−2i000000−i2−i2i2i222−2−2000000000000
χ332-222-2-22-2-202020-20i2i2−i2−i2i2i2−i2−i22-22-200i2−i2i2−i200002i2i−2i−2i22−2−222−2−22i−2i000000002−22−2i2−i2i2−i2000000000000
χ342-222-2-22-2-202020-20i2i2−i2−i2i2i2−i2−i22-22-200i2−i2i2−i20000−2i−2i2i2i−2−222−2−222−2i2i00000000−22−22i2−i2i2−i2000000000000
χ352-222-2-22-2-202020-20i2i2−i2−i2i2i2−i2−i2-22-2200i2−i2i2−i200002i2i−2i−2i22−2−222−2−2−2i2i00000000−22−22−i2i2−i2i2000000000000
χ362-222-2-22-2-202020-20i2i2−i2−i2i2i2−i2−i2-22-2200i2−i2i2−i20000−2i−2i2i2i−2−222−2−2222i−2i000000002−22−2−i2i2−i2i2000000000000
χ372-222-2-22-2-202020-20−i2−i2i2i2−i2−i2i2i22-22-200−i2i2−i2i200002i2i−2i−2i−2−222−2−2222i−2i00000000−22−22−i2i2−i2i2000000000000
χ382-222-2-22-2-202020-20−i2−i2i2i2−i2−i2i2i22-22-200−i2i2−i2i20000−2i−2i2i2i22−2−222−2−2−2i2i000000002−22−2−i2i2−i2i2000000000000
χ392-222-2-22-2-202020-20−i2−i2i2i2−i2−i2i2i2-22-2200−i2i2−i2i200002i2i−2i−2i−2−222−2−222−2i2i000000002−22−2i2−i2i2−i2000000000000
χ402-222-2-22-2-202020-20−i2−i2i2i2−i2−i2i2i2-22-2200−i2i2−i2i20000−2i−2i2i2i22−2−222−2−22i−2i00000000−22−22i2−i2i2−i2000000000000
χ412-22-22-2-2222-2-222-2-22i2i−2i−2i−2i−2i2i2i2-2-22-222i−2i−2i2i00000000000000000000002-20000002i−2i−2i2i000000000000
χ422-22-22-2-2222-2-222-2-22i2i−2i−2i−2i−2i2i2i-222-2-222i−2i−2i2i0000000000000000000000-22000000−2i2i2i−2i000000000000
χ432-22-22-2-2222-2-222-2-2−2i−2i2i2i2i2i−2i−2i2-2-22-22−2i2i2i−2i00000000000000000000002-2000000−2i2i2i−2i000000000000
χ442-22-22-2-2222-2-222-2-2−2i−2i2i2i2i2i−2i−2i-222-2-22−2i2i2i−2i0000000000000000000000-220000002i−2i−2i2i000000000000
χ452-22-22-2-222-2-222-2-22000000002-2-222-20000000000002i2i−2i−2i−2i−2i2i2i000000-22002i−2i−2i2i0000000000000000
χ462-22-22-2-222-2-222-2-22000000002-2-222-2000000000000−2i−2i2i2i2i2i−2i−2i000000-2200−2i2i2i−2i0000000000000000
χ472-22-22-2-222-2-222-2-2200000000-222-22-20000000000002i2i−2i−2i−2i−2i2i2i0000002-200−2i2i2i−2i0000000000000000
χ482-22-22-2-222-2-222-2-2200000000-222-22-2000000000000−2i−2i2i2i2i2i−2i−2i0000002-2002i−2i−2i2i0000000000000000
χ492-22-22-2-22-222-2-222-22i2i−2i−2i−2i−2i2i2i00002-2−2i2i2i−2i0000000000000000000000000000000000002i−2i2-2000000
χ502-22-22-2-22-222-2-222-22i2i−2i−2i−2i−2i2i2i00002-2−2i2i2i−2i000000000000000000000000000000000000−2i2i-22000000
χ512-22-22-2-22-222-2-222-2−2i−2i2i2i2i2i−2i−2i00002-22i−2i−2i2i0000000000000000000000000000000000002i−2i-22000000
χ522-22-22-2-22-222-2-222-2−2i−2i2i2i2i2i−2i−2i00002-22i−2i−2i2i000000000000000000000000000000000000−2i2i2-2000000
χ532-2-2-2-22220-20-202022-22-22-22-200000000002−22−22−22−22−22−22−22−200002-2002-2000000000000002−22−200
χ542-2-2-2-22220-20-202022-22-22-22-200000000002−22−22−22−22−22−22−22−20000-2200-2200000000000000−22−2200
χ552-2-2-2-22220-20-202022-22-22-22-20000000000−22−22−22−22−22−22−22−2200002-2002-200000000000000−22−2200
χ562-2-2-2-22220-20-202022-22-22-22-20000000000−22−22−22−22−22−22−22−220000-2200-22000000000000002−22−200
χ572-2-2-2-22220-20-20202-22-22-22-2200000000002−22−22−22−2−22−22−22−2200002-200-2200000000000000−222−200
χ582-2-2-2-22220-20-20202-22-22-22-2200000000002−22−22−22−2−22−22−22−220000-22002-2000000000000002−2−2200
χ592-2-2-2-22220-20-20202-22-22-22-220000000000−22−22−22−222−22−22−22−200002-200-22000000000000002−2−2200
χ602-2-2-2-22220-20-20202-22-22-22-220000000000−22−22−22−222−22−22−22−20000-22002-200000000000000−222−200
χ6144444444-4-4-4-4-4-4-4-40000000000004400000000000000000000000000000000000000000000000000
χ62444-4-44-4-44040-40-4022222222−22−22−22−22000000−22−2222220000000000000000000000000000000000000000000000
χ63444-4-44-4-44040-40-40−22−22−22−22222222220000002222−22−220000000000000000000000000000000000000000000000
χ6444-44-4-4-44040-40-404000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ6544-44-4-4-44040-40-40400000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ6644-44-4-4-440-404040-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ6744-44-4-4-440-404040-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ6844-4-44-44-4000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000002i2−2i2−2i22i22-2-222-2-22000000000000000000000000000000
χ6944-4-44-44-4000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000−2i22i22i2−2i2-222-2-222-2000000000000000000000000000000
χ7044-4-44-44-400000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000002i2−2i2−2i22i2-222-2-222-2000000000000000000000000000000
χ7144-4-44-44-400000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000−2i22i22i2−2i22-2-222-2-22000000000000000000000000000000
χ724-444-4-44-440-40-40402i22i2−2i2−2i22i22i2−2i2−2i2000000−2i22i2−2i22i20000000000000000000000000000000000000000000000
χ734-444-4-44-440-40-4040−2i2−2i22i22i2−2i2−2i22i22i20000002i2−2i22i2−2i20000000000000000000000000000000000000000000000
χ744-44-44-4-44-4-444-4-444000000000000-4400000000000000000000000000000000000000000000000000
χ754-4-4444-4-40000000022−2222−22−2222−222200000000002i2−2i2−2i22i200002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ764-4-4444-4-40000000022−2222−22−2222−22220000000000−2i22i22i2−2i20000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ774-4-4444-4-400000000−2222−222222−2222−2200000000002i2−2i2−2i22i20000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ784-4-4444-4-400000000−2222−222222−2222−220000000000−2i22i22i2−2i200002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ794-4-4-4-444404040-40-400000000000000000022−2222−22−2222−222200000000000000000000000000000000000000
χ804-4-4-4-444404040-40-4000000000000000000−2222−222222−2222−2200000000000000000000000000000000000000

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