Finite Group Databasebeta

← Group #307498

Character table — Group #307498

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822444444448888888888888888444444888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-11111-1-11-1
χ911111111111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ1011111111111111111-1-1-1-11111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1-111-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1-11111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1111-1-111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1111-1-1-1-1111-1
χ172222222222-2-222-2-2-20000-22222-2-2-2-222220000000000000000000000-2-20000000000
χ182222222222-2-222-2-2-20000-22222-2-2-2-2-2-2-2-20000000000000000000000220000000000
χ192222222222-2-222-2-2-20000-2-2-2-2-2222222-2-20000000000000000000000-220000000000
χ202222222222-2-222-2-2-20000-2-2-2-2-22222-2-22200000000000000000000002-20000000000
χ2122222222-2-222-2-222-22222-2000000000000-2-222-2-222-2-2000000000000000000000000
χ2222222222-2-222-2-222-22222-2000000000000-2-2-2-222-2-222000000000000000000000000
χ2322222222-2-222-2-222-2-2-2-2-2-20000000000002222-2-2-2-222000000000000000000000000
χ2422222222-2-222-2-222-2-2-2-2-2-200000000000022-2-22222-2-2000000000000000000000000
χ2522-22-2-22-2002-2002-2022-2-20i2i2−i2−i2i2i2−i2−i2000000002-2002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000
χ2622-22-2-22-2002-2002-2022-2-20i2i2−i2−i2i2i2−i2−i200000000-2200-22i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ2722-22-2-22-2002-2002-2022-2-20−i2−i2i2i2−i2−i2i2i2000000002-2002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000
χ2822-22-2-22-2002-2002-2022-2-20−i2−i2i2i2−i2−i2i2i200000000-2200-22−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ2922-22-2-22-2002-2002-20-2-2220i2i2−i2−i2i2i2−i2−i2000000002-200-22−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ3022-22-2-22-2002-2002-20-2-2220i2i2−i2−i2i2i2−i2−i200000000-22002-2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ3122-22-2-22-2002-2002-20-2-2220−i2−i2i2i2−i2−i2i2i2000000002-200-22i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ3222-22-2-22-2002-2002-20-2-2220−i2−i2i2i2−i2−i2i2i200000000-22002-2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ332-222-2-2-22002-200-2202i−2i2i−2i0i2−i2i2−i2i2−i2i2−i20000002-2002i−2i002−22−2i2−i2i2−i22−22−2000000000000
χ342-222-2-2-22002-200-2202i−2i2i−2i0i2−i2i2−i2i2−i2i2−i2000000-2200−2i2i002−22−2−i2i2−i2i2−22−22000000000000
χ352-222-2-2-22002-200-2202i−2i2i−2i0−i2i2−i2i2−i2i2−i2i20000002-2002i−2i00−22−22−i2i2−i2i2−22−22000000000000
χ362-222-2-2-22002-200-2202i−2i2i−2i0−i2i2−i2i2−i2i2−i2i2000000-2200−2i2i00−22−22i2−i2i2−i22−22−2000000000000
χ372-222-2-2-22002-200-220−2i2i−2i2i0i2−i2i2−i2i2−i2i2−i20000002-200−2i2i00−22−22i2−i2i2−i2−22−22000000000000
χ382-222-2-2-22002-200-220−2i2i−2i2i0i2−i2i2−i2i2−i2i2−i2000000-22002i−2i00−22−22−i2i2−i2i22−22−2000000000000
χ392-222-2-2-22002-200-220−2i2i−2i2i0−i2i2−i2i2−i2i2−i2i20000002-200−2i2i002−22−2−i2i2−i2i22−22−2000000000000
χ402-222-2-2-22002-200-220−2i2i−2i2i0−i2i2−i2i2−i2i2−i2i2000000-22002i−2i002−22−2i2−i2i2−i2−22−22000000000000
χ412-2-2222-2-22222-2-2-2-2-22i−2i−2i2i22-2-222-2-2200002i−2i00000000−2i2i2i−2i00000000000000000000
χ422-2-2222-2-22222-2-2-2-2-22i−2i−2i2i2-222-2-222-200002i−2i000000002i−2i−2i2i00000000000000000000
χ432-2-2222-2-22222-2-2-2-2-2−2i2i2i−2i22-2-222-2-220000−2i2i000000002i−2i−2i2i00000000000000000000
χ442-2-2222-2-22222-2-2-2-2-2−2i2i2i−2i2-222-2-222-20000−2i2i00000000−2i2i2i−2i00000000000000000000
χ452-2-2222-2-222-2-2-2-22220000-22-2-22-222-200000000000000000000000000002i−2i2i−2i000000
χ462-2-2222-2-222-2-2-2-22220000-22-2-22-222-20000000000000000000000000000−2i2i−2i2i000000
χ472-2-2222-2-222-2-2-2-22220000-2-222-22-2-2200000000000000000000000000002i−2i−2i2i000000
χ482-2-2222-2-222-2-2-2-22220000-2-222-22-2-220000000000000000000000000000−2i2i2i−2i000000
χ492-2-2222-2-2-2-22222-2-222i−2i−2i2i-2000000000000−2i2i0000000000002-2-22−2i2i2i−2i000000000000
χ502-2-2222-2-2-2-22222-2-222i−2i−2i2i-2000000000000−2i2i000000000000-222-22i−2i−2i2i000000000000
χ512-2-2222-2-2-2-22222-2-22−2i2i2i−2i-20000000000002i−2i0000000000002-2-222i−2i−2i2i000000000000
χ522-2-2222-2-2-2-22222-2-22−2i2i2i−2i-20000000000002i−2i000000000000-222-2−2i2i2i−2i000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ54444-44-4-4-44-4004-40000000000000000004-40000000000000000000000000000000000
χ55444-44-4-4-44-4004-4000000000000000000-440000000000000000000000000000000000
χ56444-44-4-4-4-4400-440000000000000000000000000000000000000000000000000022−2200
χ57444-44-4-4-4-4400-4400000000000000000000000000000000000000000000000000−222200
χ5844-44-4-44-400-4400-440000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ5944-44-4-44-400-4400-44000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ604-444-4-4-4400-44004-40000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ614-444-4-4-4400-44004-4000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ624-4-4444-4-4-4-4-4-44444-4000040000000000000000000000000000000000000000000000
χ634-4-4-44-4444-400-4400000000000000004-4000000000000000000000000000000000000
χ644-4-4-44-4444-400-440000000000000000-44000000000000000000000000000000000000
χ654-4-4-44-444-44004-400000000000000000000000000000000000000000000000022−220000
χ664-4-4-44-444-44004-4000000000000000000000000000000000000000000000000−22220000
χ6788-8-8-88-88000000000000000000000000000000000000000000000000000000000000
χ688-88-8-888-8000000000000000000000000000000000000000000000000000000000000

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