Finite Group Databasebeta

← Group #277283

Character table — Group #277283

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488888888888888888888222244444488888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
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
χ71111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-11-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-111111-111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-11-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1111111-1-1-1-11-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111111111-1-1-1-1-1111-1-111-1-1-11
χ172222222222-2-22-22-222222222-20000-2-2-2-2-20000000000000000000022220000000000-2-20000000000
χ182222222222-2-22-22-222222222-20000-2-2-2-2-200000000000000000000-2-2-2-20000000000220000000000
χ192222222222-2-22-22-2-2-2-2-2-2-2-2-2-20000-222220000000000000000000022-2-20000000000-220000000000
χ202222222222-2-22-22-2-2-2-2-2-2-2-2-2-20000-2222200000000000000000000-2-22200000000002-20000000000
χ2122222222-2-222-22-2200000000-22222-200002222-2-2-2-200000000-2-2-2-200002200000000000000000000
χ2222222222-2-222-22-2200000000-22222-20000-2-2-2-2222200000000-2-2220000-2-200000000000000000000
χ2322222222-2-222-22-2200000000-2-2-2-2-2-200002222-2-2-2-20000000022220000-2-200000000000000000000
χ2422222222-2-222-22-2200000000-2-2-2-2-2-20000-2-2-2-222220000000022-2-200002200000000000000000000
χ2522-22-22-2-22-200-20202222-2-2-2-2000000000022−2−222−2−22222−2−2−2−200002i−2i2i−2i0000000000000000i2−i2i2−i200
χ2622-22-22-2-22-200-20202222-2-2-2-2000000000022−2−222−2−22222−2−2−2−20000−2i2i−2i2i0000000000000000−i2i2−i2i200
χ2722-22-22-2-22-200-20202222-2-2-2-20000000000−2−222−2−222−2−2−2−2222200002i−2i2i−2i0000000000000000−i2i2−i2i200
χ2822-22-22-2-22-200-20202222-2-2-2-20000000000−2−222−2−222−2−2−2−222220000−2i2i−2i2i0000000000000000i2−i2i2−i200
χ2922-22-22-2-22-200-2020-2-2-2-22222000000000022−2−222−2−2−2−2−2−2222200002i−2i−2i2i0000000000000000i2−i2−i2i200
χ3022-22-22-2-22-200-2020-2-2-2-22222000000000022−2−222−2−2−2−2−2−222220000−2i2i2i−2i0000000000000000−i2i2i2−i200
χ3122-22-22-2-22-200-2020-2-2-2-222220000000000−2−222−2−2222222−2−2−2−200002i−2i−2i2i0000000000000000−i2i2i2−i200
χ3222-22-22-2-22-200-2020-2-2-2-222220000000000−2−222−2−2222222−2−2−2−20000−2i2i2i−2i0000000000000000i2−i2−i2i200
χ3322-2-2-2-222002-2020-222−2−222−2−202i2i−2i−2i022−2−22-22-2000022−2−222−2−2000000002i−2ii2i2−i2−i2i2i2−i2−i2000000000000
χ3422-2-2-2-222002-2020-222−2−222−2−202i2i−2i−2i022−2−2-22-220000−2−222−2−22200000000−2i2ii2i2−i2−i2−i2−i2i2i2000000000000
χ3522-2-2-2-222002-2020-222−2−222−2−20−2i−2i2i2i022−2−22-22-2000022−2−222−2−200000000−2i2i−i2−i2i2i2−i2−i2i2i2000000000000
χ3622-2-2-2-222002-2020-222−2−222−2−20−2i−2i2i2i022−2−2-22-220000−2−222−2−222000000002i−2i−i2−i2i2i2i2i2−i2−i2000000000000
χ3722-2-2-2-222002-2020-2−2−222−2−22202i2i−2i−2i0−2−2222-22-20000−2−222−2−222000000002i−2i−i2−i2i2i2−i2−i2i2i2000000000000
χ3822-2-2-2-222002-2020-2−2−222−2−22202i2i−2i−2i0−2−222-22-22000022−2−222−2−200000000−2i2i−i2−i2i2i2i2i2−i2−i2000000000000
χ3922-2-2-2-222002-2020-2−2−222−2−2220−2i−2i2i2i0−2−2222-22-20000−2−222−2−22200000000−2i2ii2i2−i2−i2i2i2−i2−i2000000000000
χ4022-2-2-2-222002-2020-2−2−222−2−2220−2i−2i2i2i0−2−222-22-22000022−2−222−2−2000000002i−2ii2i2−i2−i2−i2−i2i2i2000000000000
χ412-22-2-22-2222-2-2-22-220000000022-22-2-20000000000002i−2i2i−2i2i−2i2i−2i2-20000000000002i−2i2i−2i000000000000
χ422-22-2-22-2222-2-2-22-220000000022-22-2-2000000000000−2i2i−2i2i−2i2i−2i2i2-2000000000000−2i2i−2i2i000000000000
χ432-22-2-22-2222-2-2-22-22000000002-22-22-20000000000002i−2i2i−2i2i−2i2i−2i-22000000000000−2i2i−2i2i000000000000
χ442-22-2-22-2222-2-2-22-22000000002-22-22-2000000000000−2i2i−2i2i−2i2i−2i2i-220000000000002i−2i2i−2i000000000000
χ452-22-2-22-22-2-2222-22-22-22-22-22-220000-22-22-20000000000000000000000000000000000002i−2i2i−2i000000
χ462-22-2-22-22-2-2222-22-22-22-22-22-220000-22-22-2000000000000000000000000000000000000−2i2i−2i2i000000
χ472-22-2-22-22-2-2222-22-2-22-22-22-2220000-2-22-220000000000000000000000000000000000002i−2i−2i2i000000
χ482-22-2-22-22-2-2222-22-2-22-22-22-2220000-2-22-22000000000000000000000000000000000000−2i2i2i−2i000000
χ492-22-2-22-22-2-2-2-222222-22-22-22-2-22-22-22-22-220000000000000000-22000000002-22-20000000000000000
χ502-22-2-22-22-2-2-2-222222-22-22-22-2-2-22-222-22-2200000000000000002-200000000-22-220000000000000000
χ512-22-2-22-22-2-2-2-22222-22-22-22-22-22-22-222-22-20000000000000000-2200000000-22-220000000000000000
χ522-22-2-22-22-2-2-2-22222-22-22-22-22-2-22-2222-22-200000000000000002-2000000002-22-20000000000000000
χ532-2-222-2-2200-22020-22−2−222−2−2202i−2i−2i2i0−222−200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i2002-2000000i2−i2−i2i2−222−2000000000000
χ542-2-222-2-2200-22020-22−2−222−2−2202i−2i−2i2i0−222−20000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i200-22000000i2−i2−i2i22−2−22000000000000
χ552-2-222-2-2200-22020-22−2−222−2−220−2i2i2i−2i0−222−200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i200-22000000−i2i2i2−i22−2−22000000000000
χ562-2-222-2-2200-22020-22−2−222−2−220−2i2i2i−2i0−222−20000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i2002-2000000−i2i2i2−i2−222−2000000000000
χ572-2-222-2-2200-22020-2−222−2−222−202i−2i−2i2i02−2−2200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i2002-2000000−i2i2i2−i22−2−22000000000000
χ582-2-222-2-2200-22020-2−222−2−222−202i−2i−2i2i02−2−220000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i200-22000000−i2i2i2−i2−222−2000000000000
χ592-2-222-2-2200-22020-2−222−2−222−20−2i2i2i−2i02−2−2200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i200-22000000i2−i2−i2i2−222−2000000000000
χ602-2-222-2-2200-22020-2−222−2−222−20−2i2i2i−2i02−2−220000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i2002-2000000i2−i2−i2i22−2−22000000000000
χ6144444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000
χ62444-44-4-4-4000000002222−22−22−22−222222000000000022−22−2222000022-2-2-2-222000000000000000000000000000000
χ63444-44-4-4-4000000002222−22−22−22−2222220000000000−222222−220000-2-22222-2-2000000000000000000000000000000
χ64444-44-4-4-400000000−22−2222222222−22−22000000000022−22−22220000-2-22222-2-2000000000000000000000000000000
χ65444-44-4-4-400000000−22−2222222222−22−220000000000−222222−22000022-2-2-2-222000000000000000000000000000000
χ6644-44-44-4-4-440040-400000000000000000002222−22−22−22−22222200000000000000000000000000000000000000
χ6744-44-44-4-4-440040-40000000000000000000−22−2222222222−22−2200000000000000000000000000000000000000
χ6844-4-4-4-44400-440-4042222−22−222222−22−22000000−22−2222220000000000000000000000000000000000000000000000
χ6944-4-4-4-44400-440-404−22−222222−22−2222220000002222−22−220000000000000000000000000000000000000000000000
χ704-444-4-44-40000000022−22−2222−222222−22000000000000002i2−2i2−2i22i22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ714-444-4-44-40000000022−22−2222−222222−2200000000000000−2i22i22i2−2i2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ724-444-4-44-400000000−222222−2222−22−2222000000000000002i2−2i2−2i22i2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000
χ734-444-4-44-400000000−222222−2222−22−222200000000000000−2i22i22i2−2i22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000
χ744-44-4-44-444444-4-4-4-400000000-40000400000000000000000000000000000000000000000000000000
χ754-4-444-4-44004-40-40422−22−222222−22−222200000022−22−22220000000000000000000000000000000000000000000000
χ764-4-444-4-44004-40-404−222222−22−222222−22000000−222222−220000000000000000000000000000000000000000000000
χ774-4-4-4444-44-40040-40000000000000000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ784-4-4-4444-44-40040-4000000000000000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ794-4-4-4444-4-4400-40404-44-4-44-4400000000000000000000000000000000000000000000000000000000
χ804-4-4-4444-4-4400-4040-44-444-44-400000000000000000000000000000000000000000000000000000000

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