Finite Group Databasebeta

← Group #313608

Character table — Group #313608

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888222244444488888888444444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1111-1-1-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-11-1-1-111-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1111-1-111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111-111-1-111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11-1-111-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-111111-111-1-1-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11111-11-1-11111-1-1-11
χ17222222222-22-22-22-200000000-22222-200002222-2-2-2-200000000-2-20022-2-20000000000000000000000
χ18222222222-22-22-22-200000000-22222-20000-2-2-2-2222200000000-2-200-2-2220000000000000000000000
χ19222222222-22-22-22-200000000-2-2-2-2-2-200002222-2-2-2-2000000002200-2-2220000000000000000000000
χ20222222222-22-22-22-200000000-2-2-2-2-2-20000-2-2-2-2222200000000220022-2-20000000000000000000000
χ2122222222-22-22-22-2222222222-20000-2-2-2-2-20000000000000000002200002200000000-2-20000000000
χ2222222222-22-22-22-2222222222-20000-2-2-2-2-2000000000000000000-2-20000-2-200000000220000000000
χ2322222222-22-22-22-22-2-2-2-2-2-2-2-2-20000-22222000000000000000000220000-2-200000000-220000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2-2-2-20000-22222000000000000000000-2-2000022000000002-20000000000
χ2522-22-2-2-2222-2-222-2-22i2i2i2i−2i−2i−2i−2i-222-2-222i2i−2i−2i00000000000000002-20000000000002i2i−2i−2i000000000000
χ2622-22-2-2-2222-2-222-2-22i2i2i2i−2i−2i−2i−2i-2-2-22222i2i−2i−2i0000000000000000-22000000000000−2i−2i2i2i000000000000
χ2722-22-2-2-2222-2-222-2-2−2i−2i−2i−2i2i2i2i2i-222-2-22−2i−2i2i2i00000000000000002-2000000000000−2i−2i2i2i000000000000
χ2822-22-2-2-2222-2-222-2-2−2i−2i−2i−2i2i2i2i2i-2-2-2222−2i−2i2i2i0000000000000000-220000000000002i2i−2i−2i000000000000
χ2922-22-2-2-222-2-222-2-2200000000222-2-2-20000000000002i2i2i2i−2i−2i−2i−2i-22000000002i2i−2i−2i0000000000000000
χ3022-22-2-2-222-2-222-2-2200000000222-2-2-2000000000000−2i−2i−2i−2i2i2i2i2i-2200000000−2i−2i2i2i0000000000000000
χ3122-22-2-2-222-2-222-2-22000000002-2-222-20000000000002i2i2i2i−2i−2i−2i−2i2-200000000−2i−2i2i2i0000000000000000
χ3222-22-2-2-222-2-222-2-22000000002-2-222-2000000000000−2i−2i−2i−2i2i2i2i2i2-2000000002i2i−2i−2i0000000000000000
χ3322-22-2-2-22-222-2-222-22i2i2i2i−2i−2i−2i−2i20000-2−2i−2i2i2i0000000000000000000000000000000000002i−2i2-2000000
χ3422-22-2-2-22-222-2-222-22i2i2i2i−2i−2i−2i−2i20000-2−2i−2i2i2i000000000000000000000000000000000000−2i2i-22000000
χ3522-22-2-2-22-222-2-222-2−2i−2i−2i−2i2i2i2i2i20000-22i2i−2i−2i0000000000000000000000000000000000002i−2i-22000000
χ3622-22-2-2-22-222-2-222-2−2i−2i−2i−2i2i2i2i2i20000-22i2i−2i−2i000000000000000000000000000000000000−2i2i2-2000000
χ372-2222-2-2-220-20-2020i2i2−i2−i2i2i2−i2−i202i−2i2i−2i0i2−i2i2−i22i2i−2i−2i000022−2−222−2−200002-20000i2−i2i2−i22−22−2000000000000
χ382-2222-2-2-220-20-2020i2i2−i2−i2i2i2−i2−i202i−2i2i−2i0i2−i2i2−i2−2i−2i2i2i0000−2−222−2−2220000-220000−i2i2−i2i22−22−2000000000000
χ392-2222-2-2-220-20-2020i2i2−i2−i2i2i2−i2−i20−2i2i−2i2i0i2−i2i2−i22i2i−2i−2i000022−2−222−2−20000-220000−i2i2−i2i2−22−22000000000000
χ402-2222-2-2-220-20-2020i2i2−i2−i2i2i2−i2−i20−2i2i−2i2i0i2−i2i2−i2−2i−2i2i2i0000−2−222−2−22200002-20000i2−i2i2−i2−22−22000000000000
χ412-2222-2-2-220-20-2020−i2−i2i2i2−i2−i2i2i202i−2i2i−2i0−i2i2−i2i22i2i−2i−2i0000−2−222−2−22200002-20000−i2i2−i2i2−22−22000000000000
χ422-2222-2-2-220-20-2020−i2−i2i2i2−i2−i2i2i202i−2i2i−2i0−i2i2−i2i2−2i−2i2i2i000022−2−222−2−20000-220000i2−i2i2−i2−22−22000000000000
χ432-2222-2-2-220-20-2020−i2−i2i2i2−i2−i2i2i20−2i2i−2i2i0−i2i2−i2i22i2i−2i−2i0000−2−222−2−2220000-220000i2−i2i2−i22−22−2000000000000
χ442-2222-2-2-220-20-2020−i2−i2i2i2−i2−i2i2i20−2i2i−2i2i0−i2i2−i2i2−2i−2i2i2i000022−2−222−2−200002-20000−i2i2−i2i22−22−2000000000000
χ452-22-2-22-2202020-20-22i−2i2i−2i2i−2i2i−2i00000000002−22−222−2−2i2−i2i2−i2i2−i2i2−i2002-200002i−2i000000000000002−2i2−i200
χ462-22-2-22-2202020-20-22i−2i2i−2i2i−2i2i−2i00000000002−22−222−2−2i2−i2i2−i2i2−i2i2−i200-220000−2i2i00000000000000−22−i2i200
χ472-22-2-22-2202020-20-22i−2i2i−2i2i−2i2i−2i0000000000−22−22−2−222−i2i2−i2i2−i2i2−i2i2002-200002i−2i00000000000000−22−i2i200
χ482-22-2-22-2202020-20-22i−2i2i−2i2i−2i2i−2i0000000000−22−22−2−222−i2i2−i2i2−i2i2−i2i200-220000−2i2i000000000000002−2i2−i200
χ492-22-2-22-2202020-20-2−2i2i−2i2i−2i2i−2i2i00000000002−22−222−2−2−i2i2−i2i2−i2i2−i2i2002-20000−2i2i000000000000002−2−i2i200
χ502-22-2-22-2202020-20-2−2i2i−2i2i−2i2i−2i2i00000000002−22−222−2−2−i2i2−i2i2−i2i2−i2i200-2200002i−2i00000000000000−22i2−i200
χ512-22-2-22-2202020-20-2−2i2i−2i2i−2i2i−2i2i0000000000−22−22−2−222i2−i2i2−i2i2−i2i2−i2002-20000−2i2i00000000000000−22i2−i200
χ522-22-2-22-2202020-20-2−2i2i−2i2i−2i2i−2i2i0000000000−22−22−2−222i2−i2i2−i2i2−i2i2−i200-2200002i−2i000000000000002−2−i2i200
χ532-2-22-222-22020-20-2022−2−2−2−22202i−2i−2i2i02−2−2200002i−2i2i−2ii2i2−i2−i2−i2−i2i2i20000002-200−222−2−i2i2i2−i2000000000000
χ542-2-22-222-22020-20-2022−2−2−2−22202i−2i−2i2i02−2−220000−2i2i−2i2i−i2−i2i2i2i2i2−i2−i2000000-22002−2−22−i2i2i2−i2000000000000
χ552-2-22-222-22020-20-2022−2−2−2−2220−2i2i2i−2i02−2−2200002i−2i2i−2ii2i2−i2−i2−i2−i2i2i2000000-22002−2−22i2−i2−i2i2000000000000
χ562-2-22-222-22020-20-2022−2−2−2−2220−2i2i2i−2i02−2−220000−2i2i−2i2i−i2−i2i2i2i2i2−i2−i20000002-200−222−2i2−i2−i2i2000000000000
χ572-2-22-222-22020-20-20−2−22222−2−202i−2i−2i2i0−222−200002i−2i2i−2i−i2−i2i2i2i2i2−i2−i20000002-2002−2−22i2−i2−i2i2000000000000
χ582-2-22-222-22020-20-20−2−22222−2−202i−2i−2i2i0−222−20000−2i2i−2i2ii2i2−i2−i2−i2−i2i2i2000000-2200−222−2i2−i2−i2i2000000000000
χ592-2-22-222-22020-20-20−2−22222−2−20−2i2i2i−2i0−222−200002i−2i2i−2i−i2−i2i2i2i2i2−i2−i2000000-2200−222−2−i2i2i2−i2000000000000
χ602-2-22-222-22020-20-20−2−22222−2−20−2i2i2i−2i0−222−20000−2i2i−2i2ii2i2−i2−i2−i2−i2i2i20000002-2002−2−22−i2i2i2−i2000000000000
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ62444-4-4-44-40000000022−22−222222−22−222200000000002i2−2i2−2i22i20000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ63444-4-4-44-40000000022−22−222222−22−22220000000000−2i22i22i2−2i200002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ64444-4-4-44-400000000−222222−22−222222−2200000000002i2−2i2−2i22i200002i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ65444-4-4-44-400000000−222222−22−222222−220000000000−2i22i22i2−2i20000−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ6644-44-4-4-44-4-444-4-44400000000-40000400000000000000000000000000000000000000000000000000
χ6744-4-444-4-4000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000002i2−2i2−2i22i2-222-22-2-22000000000000000000000000000000
χ6844-4-444-4-4000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000−2i22i22i2−2i22-2-22-222-2000000000000000000000000000000
χ6944-4-444-4-400000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000002i2−2i2−2i22i22-2-22-222-2000000000000000000000000000000
χ7044-4-444-4-400000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000−2i22i22i2−2i2-222-22-2-22000000000000000000000000000000
χ714-4444-4-4-4-404040-402i22i2−2i2−2i22i22i2−2i2−2i2000000−2i22i2−2i22i20000000000000000000000000000000000000000000000
χ724-4444-4-4-4-404040-40−2i2−2i22i22i2−2i2−2i22i22i20000002i2−2i22i2−2i20000000000000000000000000000000000000000000000
χ734-44-4-44-440-40-4040400000000000000000022−2222−22−22−22222200000000000000000000000000000000000000
χ744-44-4-44-440-40-40404000000000000000000−2222−22222222−22−2200000000000000000000000000000000000000
χ754-4-44-444-4-40-4040402222−22−22−22−222222000000−222222−220000000000000000000000000000000000000000000000
χ764-4-44-444-4-40-404040−22−2222222222−22−2200000022−22−22220000000000000000000000000000000000000000000000
χ774-4-4-44-444040-40-4044-44-4-44-4400000000000000000000000000000000000000000000000000000000
χ784-4-4-44-444040-40-404-44-444-44-400000000000000000000000000000000000000000000000000000000
χ794-4-4-44-4440-404040-40000000000000000000000000022−2222−22−2222−2222000000000000000000000000000000
χ804-4-4-44-4440-404040-400000000000000000000000000−2222−222222−2222−22000000000000000000000000000000

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