Finite Group Databasebeta

← Group #277447

Character table — Group #277447

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822444444448888888888888888444444888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-111-1-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-11-1-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111-111-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-11111-1-11-1
χ911111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ1011111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111111-1-1-111-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-11111-1111-1-111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11-1-1-11111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1111-1-1-1-1111-1
χ172222222222-2-22-22-2-20000-22222-2-2-2-200002222000000000000000000-2-20000000000
χ182222222222-2-22-22-2-20000-22222-2-2-2-20000-2-2-2-2000000000000000000220000000000
χ192222222222-2-22-22-2-20000-2-2-2-2-22222000022-2-2000000000000000000-220000000000
χ202222222222-2-22-22-2-20000-2-2-2-2-222220000-2-2220000000000000000002-20000000000
χ2122222222-2-222-22-22-22222-20000000022-2-20000-2-2-2-200002200000000000000000000
χ2222222222-2-222-22-22-22222-200000000-2-2220000-2-2220000-2-200000000000000000000
χ2322222222-2-222-22-22-2-2-2-2-2-20000000022-2-2000022220000-2-200000000000000000000
χ2422222222-2-222-22-22-2-2-2-2-2-200000000-2-222000022-2-200002200000000000000000000
χ2522-2-2-2-222002-2020-202i2i−2i−2i022−2−222−2−2002i−2i0000002-2i2i2−i2−i200i2i2−i2−i222−2−2000000000000
χ2622-2-2-2-222002-2020-202i2i−2i−2i022−2−222−2−200−2i2i000000-22i2i2−i2−i200−i2−i2i2i2−2−222000000000000
χ2722-2-2-2-222002-2020-202i2i−2i−2i0−2−222−2−222002i−2i0000002-2−i2−i2i2i200−i2−i2i2i2−2−222000000000000
χ2822-2-2-2-222002-2020-202i2i−2i−2i0−2−222−2−22200−2i2i000000-22−i2−i2i2i200i2i2−i2−i222−2−2000000000000
χ2922-2-2-2-222002-2020-20−2i−2i2i2i022−2−222−2−2002i−2i000000-22−i2−i2i2i200i2i2−i2−i2−2−222000000000000
χ3022-2-2-2-222002-2020-20−2i−2i2i2i022−2−222−2−200−2i2i0000002-2−i2−i2i2i200−i2−i2i2i222−2−2000000000000
χ3122-2-2-2-222002-2020-20−2i−2i2i2i0−2−222−2−222002i−2i000000-22i2i2−i2−i200−i2−i2i2i222−2−2000000000000
χ3222-2-2-2-222002-2020-20−2i−2i2i2i0−2−222−2−22200−2i2i0000002-2i2i2−i2−i200i2i2−i2−i2−2−222000000000000
χ332-222-2-22-222-2-2-22-2222-22-2-200000000000000002-2000000002i−2i2i−2i2i−2i2i−2i000000000000
χ342-222-2-22-222-2-2-22-2222-22-2-200000000000000002-200000000−2i2i−2i2i−2i2i−2i2i000000000000
χ352-222-2-22-222-2-2-22-222-22-22-20000000000000000-22000000002i−2i2i−2i−2i2i−2i2i000000000000
χ362-222-2-22-222-2-2-22-222-22-22-20000000000000000-2200000000−2i2i−2i2i2i−2i2i−2i000000000000
χ372-222-2-22-2-2-2222-22-220000-22-22-22-22-200000000000000000000000000002i−2i2i−2i000000
χ382-222-2-22-2-2-2222-22-220000-22-22-22-22-20000000000000000000000000000−2i2i−2i2i000000
χ392-222-2-22-2-2-2222-22-220000-2-22-22-22-2200000000000000000000000000002i−2i−2i2i000000
χ402-222-2-22-2-2-2222-22-220000-2-22-22-22-220000000000000000000000000000−2i2i2i−2i000000
χ412-222-2-22-2-2-2-2-22222-22-22-222-22-2-22-2200000000-22002-22-20000000000000000000000
χ422-222-2-22-2-2-2-2-22222-22-22-22-22-222-22-200000000-2200-22-220000000000000000000000
χ432-222-2-22-2-2-2-2-22222-2-22-2222-22-2-22-22000000002-200-22-220000000000000000000000
χ442-222-2-22-2-2-2-2-22222-2-22-222-22-222-22-2000000002-2002-22-20000000000000000000000
χ452-2-2-2222-200-22020-202i−2i−2i2i02−2−22−222−22-20000000000i2−i2−i2i22i−2i2−2−22−i2i2i2−i2000000000000
χ462-2-2-2222-200-22020-202i−2i−2i2i02−2−22−222−2-220000000000i2−i2−i2i2−2i2i−222−2i2−i2−i2i2000000000000
χ472-2-2-2222-200-22020-202i−2i−2i2i0−222−22−2−222-20000000000−i2i2i2−i22i−2i−222−2i2−i2−i2i2000000000000
χ482-2-2-2222-200-22020-202i−2i−2i2i0−222−22−2−22-220000000000−i2i2i2−i2−2i2i2−2−22−i2i2i2−i2000000000000
χ492-2-2-2222-200-22020-20−2i2i2i−2i02−2−22−222−22-20000000000−i2i2i2−i2−2i2i2−2−22i2−i2−i2i2000000000000
χ502-2-2-2222-200-22020-20−2i2i2i−2i02−2−22−222−2-220000000000−i2i2i2−i22i−2i−222−2−i2i2i2−i2000000000000
χ512-2-2-2222-200-22020-20−2i2i2i−2i0−222−22−2−222-20000000000i2−i2−i2i2−2i2i−222−2−i2i2i2−i2000000000000
χ522-2-2-2222-200-22020-20−2i2i2i−2i0−222−22−2−22-220000000000i2−i2−i2i22i−2i2−2−22i2−i2−i2i2000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ54444-44-4-4-44-40040-400000000000000000004-400000000000000000000000000000000
χ55444-44-4-4-44-40040-40000000000000000000-4400000000000000000000000000000000
χ56444-44-4-4-4-4400-404000000000000000000000000000000000000000000000002i2−2i20000
χ57444-44-4-4-4-4400-40400000000000000000000000000000000000000000000000−2i22i20000
χ5844-4-4-4-44400-440-4040000002222−22−22−22−22222200000000000000000000000000000000000000
χ5944-4-4-4-44400-440-404000000−22−2222222222−22−2200000000000000000000000000000000000000
χ604-444-4-44-44444-4-4-4-4-4000040000000000000000000000000000000000000000000000
χ614-44-4-44-444-400-404000000000000000000000000000000000000000000000000022−2200
χ624-44-4-44-444-400-4040000000000000000000000000000000000000000000000000−222200
χ634-44-4-44-44-440040-40000000000000000000004i−4i000000000000000000000000000000
χ644-44-4-44-44-440040-4000000000000000000000−4i4i000000000000000000000000000000
χ654-4-4-4444-4004-40-40400000022−22−222222−22−222200000000000000000000000000000000000000
χ664-4-4-4444-4004-40-404000000−222222−22−222222−2200000000000000000000000000000000000000
χ6788-88-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-888-8-88000000000000000000000000000000000000000000000000000000000000

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