Finite Group Databasebeta

← Group #10697467

Character table — Group #10697467

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222222222444444448888888888888888161616161616161616161616242424242424242448484848
order1222223444466612121212444466121288881212121224242424242424242244666612121212888888884444
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
χ511111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-111-1-111-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-111-1-111-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-111-1-1111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-1111111-1-1
χ9222222222222222222-2-2-2-2222222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000
χ10222222222222222222-2-2-2-22222-2-222-2-2-2-2-2-2-2-22222000000000000000000000000
χ112222222-2-2-2-2222-2-2-2-22-22-222-2-2000022-2-200000000000000000000000022-2-20000
χ122222222-2-2-2-2222-2-2-2-22-22-222-2-2000022-2-2000000000000000000000000-2-2220000
χ132222222-2-2-2-2222-2-2-2-2-22-2222-2-20000-2-2220000000000000000000022-2-200000000
χ142222222-2-2-2-2222-2-2-2-2-22-2222-2-20000-2-22200000000000000000000-2-22200000000
χ15222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1111111112-22-2-1-111-1-111000000000000
χ18222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-111111111-22-2211-1-111-1-1000000000000
χ19222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ20222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-122-2-21111-1-1-1-111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ21222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22211111111-1-1-1-10000−i3i3i3−i3−i3i3i3−i3000000000000
χ22222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-22211111111-1-1-1-10000i3−i3−i3i3i3−i3−i3i3000000000000
χ232222-2-2222-2-2222222222-2-2-2-2-2-200002-22-20000000000000000000000000000002i−2i
χ242222-2-2222-2-2222222222-2-2-2-2-2-200002-22-2000000000000000000000000000000−2i2i
χ252222-2-2222-2-22222222-2-222-2-2-2-20000-22-2200000000000000000000000000002-200
χ262222-2-2222-2-22222222-2-222-2-2-2-20000-22-220000000000000000000000000000-2200
χ272222-2-22-2-222222-2-2-2-22-2-22-2-22200002-2-220000000020-202200-2-200000000000000
χ282222-2-22-2-222222-2-2-2-22-2-22-2-22200002-2-2200000000-2020-2-2002200000000000000
χ292222-2-22-2-222222-2-2-2-2-222-2-2-2220000-222-200000000020-2002200-2-2000000000000
χ302222-2-22-2-222222-2-2-2-2-222-2-2-2220000-222-2000000000-20200-2-20022000000000000
χ312222-2-2-1-2-222-1-1-111112-2-2211-1-10000-111-1−i3−i3i3i3−i3−i3i3i320-20-1-1−i3i311i3−i3000000000000
χ322222-2-2-1-2-222-1-1-111112-2-2211-1-10000-111-1−i3−i3i3i3−i3−i3i3i3-202011i3−i3-1-1−i3i3000000000000
χ332222-2-2-1-2-222-1-1-111112-2-2211-1-10000-111-1i3i3−i3−i3i3i3−i3−i320-20-1-1i3−i311−i3i3000000000000
χ342222-2-2-1-2-222-1-1-111112-2-2211-1-10000-111-1i3i3−i3−i3i3i3−i3−i3-202011−i3i3-1-1i3−i3000000000000
χ352222-2-2-1-2-222-1-1-11111-222-211-1-100001-1-11−i3−i3i3i3i3i3−i3−i3020-2−i3i3-1-1i3−i311000000000000
χ362222-2-2-1-2-222-1-1-11111-222-211-1-100001-1-11−i3−i3i3i3i3i3−i3−i30-202i3−i311−i3i3-1-1000000000000
χ372222-2-2-1-2-222-1-1-11111-222-211-1-100001-1-11i3i3−i3−i3−i3−i3i3i3020-2i3−i3-1-1−i3i311000000000000
χ382222-2-2-1-2-222-1-1-11111-222-211-1-100001-1-11i3i3−i3−i3−i3−i3i3i30-202−i3i311i3−i3-1-1000000000000
χ392-2-22-2222-22-2-2-2222-2-200002-22-2002-2000000002-22-20000000000002−22−22−22−20000
χ402-2-22-2222-22-2-2-2222-2-200002-22-2002-2000000002-22-2000000000000−22−22−22−220000
χ412-2-22-2222-22-2-2-2222-2-200002-22-200-2200000000-22-220000000000002−22−2−22−220000
χ422-2-22-2222-22-2-2-2222-2-200002-22-200-2200000000-22-22000000000000−22−222−22−20000
χ432-2-22-222-22-22-2-22-2-22200002-2-222-20000002-22-200000000000000002−2−222−2−220000
χ442-2-22-222-22-22-2-22-2-22200002-2-222-20000002-22-20000000000000000−222−2−222−20000
χ452-2-22-222-22-22-2-22-2-22200002-2-22-22000000-22-2200000000000000002−2−22−222−20000
χ462-2-22-222-22-22-2-22-2-22200002-2-22-22000000-22-220000000000000000−222−22−2−220000
χ47444444-2-4-4-4-4-2-2-222224-44-4-2-2220000-2-22200000000000000000000000000000000
χ48444444-2-4-4-4-4-2-2-22222-44-44-2-222000022-2-200000000000000000000000000000000
χ494444-4-4-244-4-4-2-2-2-2-2-2-244-4-422220000-22-2200000000000000000000000000000000
χ504444-4-4-244-4-4-2-2-2-2-2-2-2-4-444222200002-22-200000000000000000000000000000000
χ514-4-444-444-4-44-4-4444-4-40000-44-440000000000000000000000000000000000000000
χ524-4-444-44-444-4-4-44-4-4440000-444-40000000000000000000000000000000000000000
χ534-4-444-4-24-4-4422-2-2-22200002-22-200000000−2i32i32i3−2i30000000000000000000000000000
χ544-4-444-4-24-4-4422-2-2-22200002-22-2000000002i3−2i3−2i32i30000000000000000000000000000
χ554-4-444-4-2-444-422-222-2-200002-2-22000000000000−2i32i32i3−2i3000000000000000000000000
χ564-4-444-4-2-444-422-222-2-200002-2-220000000000002i3−2i3−2i32i3000000000000000000000000
χ574-4-44-44-24-44-422-2-2-2220000-22-22004-400000000-22-22000000000000000000000000
χ584-4-44-44-24-44-422-2-2-2220000-22-2200-44000000002-22-2000000000000000000000000
χ594-4-44-44-2-44-4422-222-2-20000-222-24-4000000-22-220000000000000000000000000000
χ604-4-44-44-2-44-4422-222-2-20000-222-2-440000002-22-20000000000000000000000000000
χ6188-8-800800008-8-80000000000000000000000000000000000000000000000000000
χ6288-8-800-40000-44443−4343−43000000000000000000000000000000000000000000000000
χ6388-8-800-40000-444−4343−4343000000000000000000000000000000000000000000000000
χ648-88-80080000-88-80000000000000000000000000000000000000000000000000000
χ658-88-800-400004-4443−43−4343000000000000000000000000000000000000000000000000
χ668-88-800-400004-44−434343−43000000000000000000000000000000000000000000000000

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