Finite Group Databasebeta

← Group #10833335

Character table — Group #10833335

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222224444444444444488888888888888888888121212121616161616161616162424242424242424242424242424
order1222223444466622224444661212121244446666121212121212121212121212888848812122424242422244444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1
χ4111111111111111111111111111111-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1111
χ51111111111111111-1-111-1-1111111-1-11111-1-111-1-1-1-1-1-111111111-11-1-1-111-1-11-1-1-1-1-1-111111-1-1
χ61111111111111111-1-111-1-1111111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-11-1-1-111-1-1-1111111-1-1-1-1-111
χ71111111111111111-1-111-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-11-1111-1-111-111-1-1-1-1-1111-111
χ81111111111111111-1-111-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1111-1-1111-1-111111-1-1-11-1-1
χ911111111111111-1-111-1-111111111-1-111-1-111-1-111-1-1-1-111111111-1-11-1-1-1-111-1-1-111-1-1-11-1-1111
χ1011111111111111-1-111-1-111111111-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-11-1-1-1-111111-1-1111-111-1-1-1
χ1111111111111111-1-111-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111-11111-1-111111-1-111-1-1-1-1-1
χ1211111111111111-1-111-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-111-1-111111
χ1311111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111-1-111-1-1-1-1-111-1-111-11-1-11-1-1
χ1411111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111-1-1-1-11-1-111-1-11-111-111
χ1511111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-111-1-111111-1-1-1-11111-1-1-111
χ1611111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-111-1-11111-11111-1-1-1-1111-1-1
χ17222222-12222-1-1-122222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000222-1-1-1-1-1-100000000000000
χ18222222-12222-1-1-122222222-1-1-1-1-1-122-2-2-1-1-1-1-1-1-1-1-1-1-1-111110000-2-2-211111100000000000000
χ19222222-12222-1-1-122-2-222-2-2-1-1-1-1-1-1-2-222-1-111-1-1111111-1-1-1-10000-22-211-1-11100000000000000
χ20222222-12222-1-1-122-2-222-2-2-1-1-1-1-1-1-2-2-2-2-1-111-1-1111111111100002-22-1-111-1-100000000000000
χ21222222-12222-1-1-1-2-222-2-222-1-1-1-1-1-1-2-22211-1-111-1-11111-1-1-1-10000-2-221111-1-100000000000000
χ22222222-12222-1-1-1-2-222-2-222-1-1-1-1-1-1-2-2-2-211-1-111-1-111111111000022-2-1-1-1-11100000000000000
χ23222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1222211111111-1-1-1-1-1-1-1-100002-2-2-1-1111100000000000000
χ24222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-122-2-211111111-1-1-1-111110000-22211-1-1-1-100000000000000
χ252222-2-222-2-222222200-2-200-2-22-22-200002200-2-200000000000022000000000-20000002000-200
χ262222-2-222-2-222222200-2-200-2-22-22-200002200-2-2000000000000-2-20000000002000000-2000200
χ272222-2-222-2-22222-2-2002200-2-22-22-20000-2-20022000000000000220000000002000000-2000-200
χ282222-2-222-2-22222-2-2002200-2-22-22-20000-2-20022000000000000-2-2000000000-20000002000200
χ292222-2-22-222-2222002200-2-2-2-2-22-220000002200-2-20000000022000000000000002-2000-200000
χ302222-2-22-222-2222002200-2-2-2-2-22-220000002200-2-200000000-2-200000000000000-22000200000
χ312222-2-22-222-222200-2-20022-2-2-22-22000000-2-20022000000002200000000000000-22000-200000
χ322222-2-22-222-222200-2-20022-2-2-22-22000000-2-2002200000000-2-2000000000000002-2000200000
χ332-2-222-2222-2-2-2-22002-2002-22-22-2-220000002-2002-2000000000000000000000000002i−2i002i−2i000
χ342-2-222-2222-2-2-2-22002-2002-22-22-2-220000002-2002-200000000000000000000000000−2i2i00−2i2i000
χ352-2-222-2222-2-2-2-2200-2200-222-22-2-22000000-2200-22000000000000000000000000002i−2i00−2i2i000
χ362-2-222-2222-2-2-2-2200-2200-222-22-2-22000000-2200-2200000000000000000000000000−2i2i002i−2i000
χ372-2-222-22-2-222-2-222-2002-2002-2-222-200002-2002-20000000000000000000000002-20000000002-2
χ382-2-222-22-2-222-2-222-2002-2002-2-222-200002-2002-2000000000000000000000000-22000000000-22
χ392-2-222-22-2-222-2-22-2200-22002-2-222-20000-2200-220000000000000000000000002-2000000000-22
χ402-2-222-22-2-222-2-22-2200-22002-2-222-20000-2200-22000000000000000000000000-220000000002-2
χ412-2-22-222-22-22-2-222-22-2-22-22-22-2-2222-2002-22-2-22-2222-2-20000000000000000000000000000000
χ422-2-22-222-22-22-2-222-2-22-222-2-22-2-222-22002-2-22-222-2-2-2220000000000000000000000000000000
χ432-2-22-222-22-22-2-22-222-22-2-22-22-2-222-2200-222-22-2-22-2-2220000000000000000000000000000000
χ442-2-22-222-22-22-2-22-22-222-22-2-22-2-2222-200-22-222-22-222-2-20000000000000000000000000000000
χ452-2-22-22-1-22-2211-12-22-2-22-221-111-1-12-200-11-111-11-1-1-111−i3−i3i3i30000000−i3i3−i3i3−i3i300000000000000
χ462-2-22-22-1-22-2211-12-22-2-22-221-111-1-12-200-11-111-11-1-1-111i3i3−i3−i30000000i3−i3i3−i3i3−i300000000000000
χ472-2-22-22-1-22-2211-12-2-22-222-21-111-1-1-2200-111-11-1-1111-1-1−i3−i3i3i30000000i3−i3−i3i3i3−i300000000000000
χ482-2-22-22-1-22-2211-12-2-22-222-21-111-1-1-2200-111-11-1-1111-1-1i3i3−i3−i30000000−i3i3i3−i3−i3i300000000000000
χ492-2-22-22-1-22-2211-1-222-22-2-221-111-1-1-22001-1-11-111-111-1-1−i3−i3i3i30000000i3−i3i3−i3−i3i300000000000000
χ502-2-22-22-1-22-2211-1-222-22-2-221-111-1-1-22001-1-11-111-111-1-1i3i3−i3−i30000000−i3i3−i3i3i3−i300000000000000
χ512-2-22-22-1-22-2211-1-22-222-22-21-111-1-12-2001-11-1-11-11-1-111−i3−i3i3i30000000−i3i3i3−i3i3−i300000000000000
χ522-2-22-22-1-22-2211-1-22-222-22-21-111-1-12-2001-11-1-11-11-1-111i3i3−i3−i30000000i3−i3−i3i3−i3i300000000000000
χ534444444-4-4-4-44440000000044-4-4-4-400000000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-200000000-2-22222000000000000−2i32i3−2i32i30000000000000000000000000000000
χ55444444-2-4-4-4-4-2-2-200000000-2-222220000000000002i3−2i32i3−2i30000000000000000000000000000000
χ564444-4-4-24-4-44-2-2-24400-4-40022-22-220000-2-200220000000000000000000000000000000000000
χ574444-4-4-24-4-44-2-2-2-4-400440022-22-2200002200-2-20000000000000000000000000000000000000
χ584444-4-4-2-444-4-2-2-2004400-4-4222-22-2000000-2-2002200000000000000000000000000000000000
χ594444-4-4-2-444-4-2-2-200-4-40044222-22-20000002200-2-200000000000000000000000000000000000
χ604-44-400400004-4-400000000000000002-20000000000002-22-2−2i22i2−2i22i200000000000000000000000
χ614-44-400400004-4-400000000000000002-20000000000002-22-22i2−2i22i2−2i200000000000000000000000
χ624-44-400400004-4-40000000000000000-22000000000000-22-22−2i22i22i2−2i200000000000000000000000
χ634-44-400400004-4-40000000000000000-22000000000000-22-222i2−2i2−2i22i200000000000000000000000
χ644-4-444-4-244-4-422-2004-4004-4-22-222-2000000-2200-2200000000000000000000000000000000000
χ654-4-444-4-244-4-422-200-4400-44-22-222-20000002-2002-200000000000000000000000000000000000
χ664-4-444-4-2-4-44422-24-4004-400-222-2-220000-2200-220000000000000000000000000000000000000
χ674-4-444-4-2-4-44422-2-4400-4400-222-2-2200002-2002-20000000000000000000000000000000000000
χ684-4-44-4444-44-4-4-4400000000-4444-4-400000000000000000000000000000000000000000000000
χ694-4-44-44-24-44-422-2000000002-2-2-222000000000000−2i32i32i3−2i30000000000000000000000000000000
χ704-4-44-44-24-44-422-2000000002-2-2-2220000000000002i3−2i3−2i32i30000000000000000000000000000000
χ7188-8-80080000-88-80000000000000000000000000000000000000000000000000000000000000
χ7288-8-800-400004-44000000000000000000000000000000−2i32i32i3−2i3000000000000000000000000000
χ7388-8-800-400004-440000000000000000000000000000002i3−2i3−2i32i3000000000000000000000000000
χ748-88-800-40000-44400000000000000004-4000000000000-22-22000000000000000000000000000
χ758-88-800-40000-4440000000000000000-440000000000002-22-2000000000000000000000000000

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