Finite Group Databasebeta

← Group #10768951

Character table — Group #10768951

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888888888888888161616162424242424242424242424244848
order1222223444466612121212444466121212121212244444448888121212121212121212122424242424242424612121244444444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111-1-1-111-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111
χ6111111111111111111111111111111-1-1-111-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-111
χ91111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1111-1111-1-1-111-1-11-11111-1-1-1-11111-1-1-1-11-11-11-11-11-11-111-1-11-1
χ101111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1111-1111-1-1-111-1-11-11111-1-1-1-11111-1-1-1-11-11-1-11-11-11-11-1-111-11
χ111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1111-11-1-1-111-1-1111-1-1-1-1-11111-1-1-1-111111-11-11-11-11-11-1-1-111-11
χ121111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1111-11-1-1-111-1-1111-1-1-1-1-11111-1-1-1-111111-11-1-11-11-11-1111-1-11-1
χ131111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-11-1111-1-1-1-1111-11111-1-1-1-1-1-1-1-11111-11-111-1-111-1-11-1-1111-1
χ141111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-11-1111-1-1-1-1111-11111-1-1-1-1-1-1-1-11111-11-11-111-1-111-111-1-1-11
χ151111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-11-1-1-111111-1-11-1-1-1-1-111111111-1-1-1-1-11-111-1-111-1-1111-1-1-11
χ161111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-11-1-1-111111-1-11-1-1-1-1-111111111-1-1-1-1-11-11-111-1-111-1-1-1111-1
χ17222222222-2-222222222-2-2-22222-2-2-2-2000000000000-2-200000000000000000000002200-2-2000000
χ18222222222-2-222222222-2-2-22222-2-2-2-2000000000000-2-20000000000000000000000-2-20022000000
χ192222222-2-222222-2-2-2-2-22-2-222-2-222-2-2000000000000-2200000000000000000000002-200-22000000
χ202222222-2-222222-2-2-2-2-22-2-222-2-222-2-2000000000000-220000000000000000000000-22002-2000000
χ21222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ22222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222-2-22-2-2-2-2-2-2-1-11111111111111111-1-1-1-100000000000000
χ23222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-222-222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111100000000000000
χ24222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1111100000000000000
χ25222222-1-2-2-2-2-1-1-11111-2-222-1-11111-1-12-2222-2-2-222-2-2-11-1-1-1-11111-1-1-1-11111-11-1100000000000000
χ26222222-1-2-2-2-2-1-1-11111-2-222-1-11111-1-12-22-2-2-222-2-222-111111-1-1-1-11111-1-1-1-1-11-1100000000000000
χ27222222-1-2-2-2-2-1-1-11111-2-222-1-11111-1-1-22-2222-2-2-2-222-11-1-1-1-111111111-1-1-1-11-11-100000000000000
χ28222222-1-2-2-2-2-1-1-11111-2-222-1-11111-1-1-22-2-2-222222-2-2-111111-1-1-1-1-1-1-1-111111-11-100000000000000
χ292222-2-2222222222222-2-22-2-2-2-2-2222222-200-2000000-2-2000000000000000022-2-200000000000000
χ302222-2-2222222222222-2-22-2-2-2-2-22222-2-22002000000-2-20000000000000000-2-22200000000000000
χ312222-2-2222-2-22222222-22-22-2-2-2-2-2-2-2-200000000000022000000000000000000002200-2-200000000
χ322222-2-2222-2-22222222-22-22-2-2-2-2-2-2-2-20000000000002200000000000000000000-2-2002200000000
χ332222-2-22-2-222222-2-2-2-22-2-22-2-22222-2-20000000000002-2000000000000000000002-200-2200000000
χ342222-2-22-2-222222-2-2-2-22-2-22-2-22222-2-20000000000002-200000000000000000000-22002-200000000
χ352222-2-22-2-2-2-2222-2-2-2-2222-2-2-222-2-2222-2-2002000000-2200000000000000002-2-2200000000000000
χ362222-2-22-2-2-2-2222-2-2-2-2222-2-2-222-2-222-22200-2000000-220000000000000000-222-200000000000000
χ372222-2-2-12222-1-1-1-1-1-1-1-2-22-21111-1-1-1-122-200-200000011−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-1-11100000000000000
χ382222-2-2-12222-1-1-1-1-1-1-1-2-22-21111-1-1-1-122-200-200000011i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-1-11100000000000000
χ392222-2-2-12222-1-1-1-1-1-1-1-2-22-21111-1-1-1-1-2-2200200000011−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i311-1-100000000000000
χ402222-2-2-12222-1-1-1-1-1-1-1-2-22-21111-1-1-1-1-2-2200200000011i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i311-1-100000000000000
χ412222-2-2-1-2-2-2-2-1-1-11111222-211-1-111-1-12-2-20020000001-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-111-100000000000000
χ422222-2-2-1-2-2-2-2-1-1-11111222-211-1-111-1-12-2-20020000001-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-111-100000000000000
χ432222-2-2-1-2-2-2-2-1-1-11111222-211-1-111-1-1-22200-20000001-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i31-1-1100000000000000
χ442222-2-2-1-2-2-2-2-1-1-11111222-211-1-111-1-1-22200-20000001-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i31-1-1100000000000000
χ45444444-244-4-4-2-2-2-2-2-2-24-4-4-4-2-2-2-22222000000000000220000000000000000000000000000000000
χ46444444-2-4-444-2-2-22222-44-4-4-2-222-2-2220000000000002-20000000000000000000000000000000000
χ474444-4-4-244-4-4-2-2-2-2-2-2-2-44-4422222222000000000000-2-20000000000000000000000000000000000
χ484444-4-4-2-4-444-2-2-222224-4-4422-2-2-2-222000000000000-220000000000000000000000000000000000
χ4944-4-40044-4004-4-444-4-40000000000000000000000000000000000000000000000000000002-22-200
χ5044-4-40044-4004-4-444-4-4000000000000000000000000000000000000000000000000000000-22-2200
χ5144-4-4004-44004-4-4-4-4440000000000000000000000000000000000000000000000000000002-2-2200
χ5244-4-4004-44004-4-4-4-444000000000000000000000000000000000000000000000000000000-222-200
χ534-44-44-440000-44-4000000004-40000000000000022−2200000000000022−2222−220000000000000000000000
χ544-44-44-440000-44-4000000004-400000000000000−2222000000000000−2222−22220000000000000000000000
χ554-44-44-4-200002-2223−2323−230000-2223−2300000000000022−22000000000000−22−226−66−6000000000000000000
χ564-44-44-4-200002-2223−2323−230000-2223−23000000000000−22220000000000002−22−2−66−66000000000000000000
χ574-44-44-4-200002-22−2323−23230000-22−232300000000000022−22000000000000−22−22−66−66000000000000000000
χ584-44-44-4-200002-22−2323−23230000-22−2323000000000000−22220000000000002−22−26−66−6000000000000000000
χ594-44-4-4440000-44-400000000-440000000000000000−2i22i200000000000000−2i22i22i2−2i2000000000000000000
χ604-44-4-4440000-44-400000000-4400000000000000002i2−2i2000000000000002i2−2i2−2i22i2000000000000000000
χ614-44-4-44-200002-2223−2323−2300002-2−232300000000000000−2i22i20000000000i6−i6−i6i6i2−i2−i2i2000000000000000000
χ624-44-4-44-200002-2223−2323−2300002-2−2323000000000000002i2−2i20000000000−i6i6i6−i6−i2i2i2−i2000000000000000000
χ634-44-4-44-200002-22−2323−232300002-223−2300000000000000−2i22i20000000000−i6i6i6−i6i2−i2−i2i2000000000000000000
χ644-44-4-44-200002-22−2323−232300002-223−23000000000000002i2−2i20000000000i6−i6−i6i6−i2i2i2−i2000000000000000000
χ654-4-44004004i−4i-4-440000000000004i−4i000002i−2i02-20000002i−2i2i−2i2-22-200000000000000000000000000
χ664-4-44004004i−4i-4-440000000000004i−4i00000−2i2i0-22000000−2i2i−2i2i-22-2200000000000000000000000000
χ674-4-4400400−4i4i-4-44000000000000−4i4i000002i−2i0-220000002i−2i2i−2i-22-2200000000000000000000000000
χ684-4-4400400−4i4i-4-44000000000000−4i4i00000−2i2i02-2000000−2i2i−2i2i2-22-200000000000000000000000000
χ694-4-4400-2004i−4i22-223−23−232300000000−2i2i−2i32i30002i−2i02-20000002ζ14−2ζ142ζ22−2ζ22−1+i31−i3−1−i31+i300000000000000000000000000
χ704-4-4400-2004i−4i22-223−23−232300000000−2i2i−2i32i3000−2i2i0-22000000−2ζ142ζ14−2ζ222ζ221−i3−1+i31+i3−1−i300000000000000000000000000
χ714-4-4400-2004i−4i22-2−232323−2300000000−2i2i2i3−2i30002i−2i02-20000002ζ22−2ζ222ζ14−2ζ14−1−i31+i3−1+i31−i300000000000000000000000000
χ724-4-4400-2004i−4i22-2−232323−2300000000−2i2i2i3−2i3000−2i2i0-22000000−2ζ222ζ22−2ζ142ζ141+i3−1−i31−i3−1+i300000000000000000000000000
χ734-4-4400-200−4i4i22-223−23−2323000000002i−2i2i3−2i30002i−2i0-220000002ζ22−2ζ222ζ14−2ζ141+i3−1−i31−i3−1+i300000000000000000000000000
χ744-4-4400-200−4i4i22-223−23−2323000000002i−2i2i3−2i3000−2i2i02-2000000−2ζ222ζ22−2ζ142ζ14−1−i31+i3−1+i31−i300000000000000000000000000
χ754-4-4400-200−4i4i22-2−232323−23000000002i−2i−2i32i30002i−2i0-220000002ζ14−2ζ142ζ22−2ζ221−i3−1+i31+i3−1−i300000000000000000000000000
χ764-4-4400-200−4i4i22-2−232323−23000000002i−2i−2i32i3000−2i2i02-2000000−2ζ142ζ14−2ζ222ζ22−1+i31−i3−1−i31+i300000000000000000000000000
χ7788-8-800-48-800-444-4-444000000000000000000000000000000000000000000000000000000000000
χ7888-8-800-4-8800-44444-4-4000000000000000000000000000000000000000000000000000000000000

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