Finite Group Databasebeta

← Group #10714381

Character table — Group #10714381

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222222222444444448888888888888888161616161616161616161616242424242424242448484848
order122222344446661212121266888812122466881212242424242424242424446612121212121216161616161616164444
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-1-1-1111111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-1-1-111-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-11111-1-11111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-11111-1-1-1-1-1-1111111-1-1
χ922222222222222222222-2-2-2-2222222-2-222-2-2-2-2-2-2-2-2000000000000000000000000
χ1022222222222222222222-2-2-2-222-2-2-2-222-2-2-2-2-2-22222000000000000000000000000
χ112222222-2-2-2-2222-2-2-2-2220000-2-22-22200-2-20000000000000000000022−2−222−2−20000
χ122222222-2-2-2-2222-2-2-2-2220000-2-22-22200-2-200000000000000000000−2−222−2−2220000
χ132222222-2-2-2-2222-2-2-2-2220000-2-2-22-2-200220000000000000000000022−2−2−2−2220000
χ142222222-2-2-2-2222-2-2-2-2220000-2-2-22-2-2002200000000000000000000−2−22222−2−20000
χ15222222-12222-1-1-1-1-1-1-1-1-12222-1-122-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-12222-1-1-1-1-1-1-1-1-12222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-12222-1-1-1-1-1-1-1-1-12222-1-1-2-211-2-211-1-1-1-111112-22-2-1-11111-1-1000000000000
χ18222222-12222-1-1-1-1-1-1-1-1-12222-1-1-2-211-2-211-1-1-1-11111-22-2211-1-1-1-111000000000000
χ19222222-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-122-1-1-2-2-1-1111111110000−i3i3−i3−i3i3i3−i3i3000000000000
χ20222222-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-122-1-1-2-2-1-1111111110000i3−i3i3i3−i3−i3i3−i3000000000000
χ21222222-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-2-21122111111-1-1-1-10000−i3i3i3i3−i3−i3−i3i3000000000000
χ22222222-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-2-21122111111-1-1-1-10000i3−i3−i3−i3i3i3i3−i3000000000000
χ232222-2-222-2-22222-2-2-2-2-2-22-22-2220000000022-2-20000020-2002-22-200000000000000
χ242222-2-222-2-22222-2-2-2-2-2-22-22-2220000000022-2-200000-20200-22-2200000000000000
χ252222-2-222-2-22222-2-2-2-2-2-2-22-222200000000-2-222000020-20220000-2-2000000000000
χ262222-2-222-2-22222-2-2-2-2-2-2-22-222200000000-2-2220000-2020-2-2000022000000000000
χ272222-2-2-12-2-22-1-1-11111112-22-2-1-100−i3i300−i3i3-1-111−i3−i3i3i3020-2−i3i3-11-11i3−i3000000000000
χ282222-2-2-12-2-22-1-1-11111112-22-2-1-100−i3i300−i3i3-1-111−i3−i3i3i30-202i3−i31-11-1−i3i3000000000000
χ292222-2-2-12-2-22-1-1-11111112-22-2-1-100i3−i300i3−i3-1-111i3i3−i3−i3020-2i3−i3-11-11−i3i3000000000000
χ302222-2-2-12-2-22-1-1-11111112-22-2-1-100i3−i300i3−i3-1-111i3i3−i3−i30-202−i3i31-11-1i3−i3000000000000
χ312222-2-2-12-2-22-1-1-1111111-22-22-1-100−i3i300−i3i311-1-1i3i3−i3−i320-20-1-1−i3i3i3−i311000000000000
χ322222-2-2-12-2-22-1-1-1111111-22-22-1-100−i3i300−i3i311-1-1i3i3−i3−i3-202011i3−i3−i3i3-1-1000000000000
χ332222-2-2-12-2-22-1-1-1111111-22-22-1-100i3−i300i3−i311-1-1−i3−i3i3i320-20-1-1i3−i3−i3i311000000000000
χ342222-2-2-12-2-22-1-1-1111111-22-22-1-100i3−i300i3−i311-1-1−i3−i3i3i3-202011−i3i3i3−i3-1-1000000000000
χ352-22-22-22-22-22-2-2222-2-22-22-2-22-22000000002-22-2000000000000000000000000002i−2i
χ362-22-22-22-22-22-2-2222-2-22-22-2-22-22000000002-22-200000000000000000000000000−2i2i
χ372-22-22-22-22-22-2-2222-2-22-2-222-2-2200000000-22-220000000000000000000000002i−2i00
χ382-22-22-22-22-22-2-2222-2-22-2-222-2-2200000000-22-22000000000000000000000000−2i2i00
χ392-22-2-22222-2-2-2-2222-2-2-2200002-200002i−2i0000002i−2i2i−2i000000000000−i2i2−i2i22−22−20000
χ402-22-2-22222-2-2-2-2222-2-2-2200002-200002i−2i0000002i−2i2i−2i000000000000i2−i2i2−i2−22−220000
χ412-22-2-22222-2-2-2-2222-2-2-2200002-20000−2i2i000000−2i2i−2i2i000000000000−i2i2−i2i2−22−220000
χ422-22-2-22222-2-2-2-2222-2-2-2200002-20000−2i2i000000−2i2i−2i2i000000000000i2−i2i2−i22−22−20000
χ432-22-2-222-2-222-2-22-2-222-2222-2-2-22000000002-2-2200000000000000002i−2i−2i2i00000000
χ442-22-2-222-2-222-2-22-2-222-2222-2-2-22000000002-2-220000000000000000−2i2i2i−2i00000000
χ452-22-2-222-2-222-2-22-2-222-22-2-222-2200000000-222-2000000000000000000002-2-220000
χ462-22-2-222-2-222-2-22-2-222-22-2-222-2200000000-222-200000000000000000000-222-20000
χ47444444-2-4-4-4-4-2-2-22222-2-20000224-4-2-2002200000000000000000000000000000000
χ48444444-2-4-4-4-4-2-2-22222-2-2000022-442200-2-200000000000000000000000000000000
χ494444-4-44-444-44444444-4-40000-4-40000000000000000000000000000000000000000
χ504444-4-4-2-444-4-2-2-2-2-2-2-22200002200−2i32i3002i3−2i300000000000000000000000000000000
χ514444-4-4-2-444-4-2-2-2-2-2-2-222000022002i3−2i300−2i32i300000000000000000000000000000000
χ524-44-44-444-44-4-4-44-4-4444-400004-40000000000000000000000000000000000000000
χ534-44-44-4-24-44-422-222-2-2-220000-2200000000000023−23−2323000000000000000000000000
χ544-44-44-4-24-44-422-222-2-2-220000-22000000000000−232323−23000000000000000000000000
χ554-44-44-4-2-44-4422-2-2-222-224-4-442-200000000-22-220000000000000000000000000000
χ564-44-44-4-2-44-4422-2-2-222-22-444-42-2000000002-22-20000000000000000000000000000
χ574-44-4-44-244-4-422-2-2-2222-20000-2200004i−4i000000−2i2i−2i2i000000000000000000000000
χ584-44-4-44-244-4-422-2-2-2222-20000-220000−4i4i0000002i−2i2i−2i000000000000000000000000
χ594-44-4-44-2-4-44422-222-2-22-244-4-42-200000000-222-20000000000000000000000000000
χ604-44-4-44-2-4-44422-222-2-22-2-4-4442-2000000002-2-220000000000000000000000000000
χ6188-8-800800008-8-80000000000000000000000000000000000000000000000000000
χ6288-8-800-40000-44443−4343−43000000000000000000000000000000000000000000000000
χ6388-8-800-40000-444−4343−4343000000000000000000000000000000000000000000000000
χ648-8-880080000-88-80000000000000000000000000000000000000000000000000000
χ658-8-8800-400004-4443−43−4343000000000000000000000000000000000000000000000000
χ668-8-8800-400004-44−434343−43000000000000000000000000000000000000000000000000

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