Finite Group Databasebeta

← Group #10695921

Character table — Group #10695921

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222222222224444444444488888888888888888888888888161616161616242424242424242448484848
order12222234444446661212121244466121212121212224466668888121212121212242424242424242424661212444488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ92222222222-2-222222222-2-2-222-2-222-2-2000000000000-2-200000000000000000022-2-200000000
χ102222222222-2-222222222-2-2-222-2-222-2-2000000000000-2-2000000000000000000-2-22200000000
χ112222222-2-2-222-2222-2-2-2-22-2-22222-2-2-2-20000000000002-2000000000000000000000000002-200
χ122222222-2-2-222-2222-2-2-2-22-2-22222-2-2-2-20000000000002-200000000000000000000000000-2200
χ132222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-22222-2-222220000-22-2-2-2-200000000000000000000000000
χ142222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-222-2-222-2-2-2-20000-22222200000000000000000000000000
χ15222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1000000000000
χ16222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111-2-21111000000000000
χ17222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-211112222-1-11111-1-1-1-1-1-1-1-1-2-21111000000000000
χ18222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-2-1-111111111111122-1-1-1-1000000000000
χ19222222-1-2-2-2-2-2-2-1-1-11111-222-1-11111-1-122-2-2-1-1-1-100001-11111−i3−i3−i3−i3i3i3i3i300−i3i3−i3i3000000000000
χ20222222-1-2-2-2-2-2-2-1-1-11111-222-1-11111-1-122-2-2-1-1-1-100001-11111i3i3i3i3−i3−i3−i3−i300i3−i3i3−i3000000000000
χ21222222-1-2-2-2-2-2-2-1-1-11111-222-1-11111-1-1-2-222111100001-1-1-1-1-1−i3−i3−i3−i3i3i3i3i300i3−i3i3−i3000000000000
χ22222222-1-2-2-2-2-2-2-1-1-11111-222-1-11111-1-1-2-222111100001-1-1-1-1-1i3i3i3i3−i3−i3−i3−i300−i3i3−i3i3000000000000
χ232222-2-2222-222-22222222-2-22-2-222-2-2220000000022-2-2-2-2000022-2-222-2-2000000000000000000
χ242222-2-2222-222-22222222-2-22-2-222-2-22200000000-2-222-2-20000-2-222-2-222000000000000000000
χ252222-2-2222-2-2-2-2222222222-2-2-2-2-2-2-2-2-20000000000002200000000000000000000002i2i−2i−2i0000
χ262222-2-2222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2000000000000220000000000000000000000−2i−2i2i2i0000
χ272222-2-22-2-22222222-2-2-2-2-22-2-2-22222-2-2000000000000-2200000000000000000000000000002-2
χ282222-2-22-2-22222222-2-2-2-2-22-2-2-22222-2-2000000000000-220000000000000000000000000000-22
χ292222-2-22-2-22-2-22222-2-2-2-22-22-2-2-2-222220000000000002-20000000000002-222-2-2000000000000
χ302222-2-22-2-22-2-22222-2-2-2-22-22-2-2-2-222220000000000002-2000000000000-22-2-222000000000000
χ312222-2-2-122-222-2-1-1-1-1-1-1-1-2-2211-1-111-1-10000−i3−i3i3i322-2-211−i3−i3i3i3-1-111-1-11100−i3i3i3−i3000000000000
χ322222-2-2-122-222-2-1-1-1-1-1-1-1-2-2211-1-111-1-10000−i3−i3i3i3-2-22211−i3−i3i3i311-1-111-1-100i3−i3−i3i3000000000000
χ332222-2-2-122-222-2-1-1-1-1-1-1-1-2-2211-1-111-1-10000i3i3−i3−i322-2-211i3i3−i3−i3-1-111-1-11100i3−i3−i3i3000000000000
χ342222-2-2-122-222-2-1-1-1-1-1-1-1-2-2211-1-111-1-10000i3i3−i3−i3-2-22211i3i3−i3−i311-1-111-1-100−i3i3i3−i3000000000000
χ352222-2-2-1-2-22-2-22-1-1-111112-221111-1-1-1-10000−i3−i3i3i30000-11i3i3−i3−i3−i3−i3i3i3i3i3−i3−i32-2-1-111000000000000
χ362222-2-2-1-2-22-2-22-1-1-111112-221111-1-1-1-10000−i3−i3i3i30000-11i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3-2211-1-1000000000000
χ372222-2-2-1-2-22-2-22-1-1-111112-221111-1-1-1-10000i3i3−i3−i30000-11−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-2211-1-1000000000000
χ382222-2-2-1-2-22-2-22-1-1-111112-221111-1-1-1-10000i3i3−i3−i30000-11−i3−i3i3i3i3i3−i3−i3−i3−i3i3i32-2-1-111000000000000
χ392-2-222-222-2200-2-2-2222-2-20002-2002-200000000002−22−20000002−22−22−22−20000002i−2i00−i2i2−i2i20000
χ402-2-222-222-2200-2-2-2222-2-20002-2002-200000000002−22−20000002−22−22−22−2000000−2i2i00i2−i2i2−i20000
χ412-2-222-222-2200-2-2-2222-2-20002-2002-20000000000−22−22000000−22−22−22−220000002i−2i00i2−i2i2−i20000
χ422-2-222-222-2200-2-2-2222-2-20002-2002-20000000000−22−22000000−22−22−22−22000000−2i2i00−i2i2−i2i20000
χ432-2-22-2222-2-2002-2-2222-2-2000-2200-2200000000002−2−220000002−2−222−2−22000000002-22−2−220000
χ442-2-22-2222-2-2002-2-2222-2-2000-2200-2200000000002−2−220000002−2−222−2−2200000000-22−222−20000
χ452-2-22-2222-2-2002-2-2222-2-2000-2200-220000000000−222−2000000−222−2−222−2000000002-2−222−20000
χ462-2-22-2222-2-2002-2-2222-2-2000-2200-220000000000−222−2000000−222−2−222−200000000-222−2−220000
χ47444444-2444-4-44-2-2-2-2-2-2-2-4-4-4-2-222-2-22200000000000022000000000000000000000000000000
χ48444444-2-4-4-444-4-2-2-222224-4-4-2-2-2-22222000000000000-22000000000000000000000000000000
χ494444-4-4-244-4-4-4-4-2-2-2-2-2-2-244-422222222000000000000-2-2000000000000000000000000000000
χ504444-4-4-2-4-44444-2-2-22222-44-422-2-2-2-2220000000000002-2000000000000000000000000000000
χ514-44-40040004i−4i04-4-40000000004i−4i00002-22i−2i2-22-20000002i−2i2i−2i00000000000000000000000000
χ524-44-40040004i−4i04-4-40000000004i−4i0000-22−2i2i-22-22000000−2i2i−2i2i00000000000000000000000000
χ534-44-4004000−4i4i04-4-4000000000−4i4i00002-2−2i2i2-22-2000000−2i2i−2i2i00000000000000000000000000
χ544-44-4004000−4i4i04-4-4000000000−4i4i0000-222i−2i-22-220000002i−2i2i−2i00000000000000000000000000
χ554-44-400-20004i−4i0-22223−2323−2300000−2i2i00−2i32i32-22i−2i−1−i31+i3−1+i31−i30000002ζ22−2ζ222ζ14−2ζ1400000000000000000000000000
χ564-44-400-20004i−4i0-22223−2323−2300000−2i2i00−2i32i3-22−2i2i1+i3−1−i31−i3−1+i3000000−2ζ222ζ22−2ζ142ζ1400000000000000000000000000
χ574-44-400-20004i−4i0-222−2323−232300000−2i2i002i3−2i32-22i−2i−1+i31−i3−1−i31+i30000002ζ14−2ζ142ζ22−2ζ2200000000000000000000000000
χ584-44-400-20004i−4i0-222−2323−232300000−2i2i002i3−2i3-22−2i2i1−i3−1+i31+i3−1−i3000000−2ζ142ζ14−2ζ222ζ2200000000000000000000000000
χ594-44-400-2000−4i4i0-22223−2323−23000002i−2i002i3−2i32-2−2i2i−1+i31−i3−1−i31+i3000000−2ζ142ζ14−2ζ222ζ2200000000000000000000000000
χ604-44-400-2000−4i4i0-22223−2323−23000002i−2i002i3−2i3-222i−2i1−i3−1+i31+i3−1−i30000002ζ14−2ζ142ζ22−2ζ2200000000000000000000000000
χ614-44-400-2000−4i4i0-222−2323−2323000002i−2i00−2i32i32-2−2i2i−1−i31+i3−1+i31−i3000000−2ζ222ζ22−2ζ142ζ1400000000000000000000000000
χ624-44-400-2000−4i4i0-222−2323−2323000002i−2i00−2i32i3-222i−2i1+i3−1−i31−i3−1+i30000002ζ22−2ζ222ζ14−2ζ1400000000000000000000000000
χ634-4-444-44-44-4004-4-44-4-4440004-400-440000000000000000000000000000000000000000000000
χ644-4-444-4-24-4400-422-2-2-222000-2200-22000000000022−2222−22000000−22−22−22−22000000000000000000
χ654-4-444-4-24-4400-422-2-2-222000-2200-220000000000−2222−22220000002−22−22−22−2000000000000000000
χ664-4-444-4-2-44-400422-222-2-2000-22002-200000000000000000000i6−i6i6−i6−i6i6−i6i6000000000000000000
χ674-4-444-4-2-44-400422-222-2-2000-22002-200000000000000000000−i6i6−i6i6i6−i6i6−i6000000000000000000
χ684-4-44-444-44400-4-4-44-4-444000-44004-40000000000000000000000000000000000000000000000
χ694-4-44-44-24-4-400422-2-2-2220002-2002-2000000000022−22−2222000000−222−2−222−2000000000000000000
χ704-4-44-44-24-4-400422-2-2-2220002-2002-20000000000−222222−220000002−2−222−2−22000000000000000000
χ714-4-44-44-2-44400-422-222-2-20002-200-2200000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000
χ724-4-44-44-2-44400-422-222-2-20002-200-2200000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000
χ7388-8-8008000000-88-800000000000000000000000000000000000000000000000000000000000
χ7488-8-800-40000004-4443−43−43430000000000000000000000000000000000000000000000000000000
χ7588-8-800-40000004-44−434343−430000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.