Finite Group Databasebeta

← Group #10768907

Character table — Group #10768907

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222222222444444444444888888888888888888888888888888161616162424242424242424242424244848
order1222223444466612121212444466121212121212244444448888121212121212121212122424242424242424612121222444444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-11-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-11-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111-1-111-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ6111111111111111111111111111111-1-111-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111111-1-1
χ91111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-11-11111-1-1-1-11111-1-1-1-11-11-11-11-11-11-111-1-11-1
χ101111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-11-11111-1-1-1-11111-1-1-1-11-11-1-11-11-11-11-1-111-11
χ111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-111-1-1-1111-1-1-1-1-11111-1-1-1-111111-11-11-11-11-11-1-1-111-11
χ121111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-111-1-1-1111-1-1-1-1-11111-1-1-1-111111-11-1-11-11-11-1111-1-11-1
χ131111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-1-1111-1-11-1-1111-11111-1-1-1-1-1-1-1-11111-11-111-1-111-1-1111-1-1-11
χ141111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-1-1111-1-11-1-1111-11111-1-1-1-1-1-1-1-11111-11-11-111-1-111-1-1-1111-1
χ151111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-11-1-1-1-1-111111111-1-1-1-1-11-111-1-111-1-11-1-1111-1
χ161111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-11-1-1-1-1-111111111-1-1-1-1-11-11-111-1-111-111-1-1-11
χ17222222222-2-2222-2-2-2-22-2-2-222-2-222-2-2000000000000-22000000000000000000002-200-2200000000
χ18222222222-2-2222-2-2-2-22-2-2-222-2-222-2-2000000000000-2200000000000000000000-22002-200000000
χ192222222-2-2222222222-22-2-22222-2-2-2-2000000000000-2-2000000000000000000002200-2-200000000
χ202222222-2-2222222222-22-2-22222-2-2-2-2000000000000-2-200000000000000000000-2-2002200000000
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
χ22222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-2-22-2-22-2-2-2-2-1-11111111111111111-1-1-1-100000000000000
χ23222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-222-222-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111100000000000000
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
χ25222222-1-2-2-2-2-1-1-11111-2-222-1-11111-1-12222-2-2-2-222-2-2-11-1-1-1-11111-1-1-1-11111-11-1100000000000000
χ26222222-1-2-2-2-2-1-1-11111-2-222-1-11111-1-122-2-2-222-2-2-222-111111-1-1-1-11111-1-1-1-1-11-1100000000000000
χ27222222-1-2-2-2-2-1-1-11111-2-222-1-11111-1-1-2-2222-2-22-2-222-11-1-1-1-111111111-1-1-1-11-11-100000000000000
χ28222222-1-2-2-2-2-1-1-11111-2-222-1-11111-1-1-2-2-2-2222222-2-2-111111-1-1-1-1-1-1-1-111111-11-100000000000000
χ292222-2-2222222222222-2-22-2-2-2-2-222222-200-20020000-2-2000000000000000022-2-200000000000000
χ302222-2-2222222222222-2-22-2-2-2-2-22222-2200200-20000-2-20000000000000000-2-22200000000000000
χ312222-2-2222-2-2222-2-2-2-2-22-22-2-22222-2-20000000000002-200000000000000000000002-200-22000000
χ322222-2-2222-2-2222-2-2-2-2-22-22-2-22222-2-20000000000002-20000000000000000000000-22002-2000000
χ332222-2-22-2-22222222222-2-22-2-2-2-2-2-2-2-20000000000002200000000000000000000002200-2-2000000
χ342222-2-22-2-22222222222-2-22-2-2-2-2-2-2-2-2000000000000220000000000000000000000-2-20022000000
χ352222-2-22-2-2-2-2222-2-2-2-2222-2-2-222-2-2222-200200-20000-2200000000000000002-2-2200000000000000
χ362222-2-22-2-2-2-2222-2-2-2-2222-2-2-222-2-222-2200-20020000-220000000000000000-222-200000000000000
χ372222-2-2-12222-1-1-1-1-1-1-1-2-22-21111-1-1-1-12-200-2002000011−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-1-11100000000000000
χ382222-2-2-12222-1-1-1-1-1-1-1-2-22-21111-1-1-1-12-200-2002000011i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-1-11100000000000000
χ392222-2-2-12222-1-1-1-1-1-1-1-2-22-21111-1-1-1-1-2200200-2000011−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i311-1-100000000000000
χ402222-2-2-12222-1-1-1-1-1-1-1-2-22-21111-1-1-1-1-2200200-2000011i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i311-1-100000000000000
χ412222-2-2-1-2-2-2-2-1-1-11111222-211-1-111-1-12-200200-200001-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-111-100000000000000
χ422222-2-2-1-2-2-2-2-1-1-11111222-211-1-111-1-12-200200-200001-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-111-100000000000000
χ432222-2-2-1-2-2-2-2-1-1-11111222-211-1-111-1-1-2200-200200001-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i31-1-1100000000000000
χ442222-2-2-1-2-2-2-2-1-1-11111222-211-1-111-1-1-2200-200200001-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i31-1-1100000000000000
χ45444444-244-4-4-2-2-222224-4-4-4-2-222-2-2220000000000002-20000000000000000000000000000000000
χ46444444-2-4-444-2-2-2-2-2-2-2-44-4-4-2-2-2-22222000000000000220000000000000000000000000000000000
χ474444-4-4-244-4-4-2-2-22222-44-4422-2-2-2-222000000000000-220000000000000000000000000000000000
χ484444-4-4-2-4-444-2-2-2-2-2-2-24-4-4422222222000000000000-2-20000000000000000000000000000000000
χ4944-4-44-440000-44-4000000004-40000000000000022−2200000000000022−2222−220000000000000000000000
χ5044-4-44-440000-44-4000000004-400000000000000−2222000000000000−2222−22220000000000000000000000
χ5144-4-44-4-200002-222323−23−230000-2223−2300000000000022−22000000000000−22−226−66−6000000000000000000
χ5244-4-44-4-200002-222323−23−230000-2223−23000000000000−22220000000000002−22−2−66−66000000000000000000
χ5344-4-44-4-200002-22−23−2323230000-22−232300000000000022−22000000000000−22−22−66−66000000000000000000
χ5444-4-44-4-200002-22−23−2323230000-22−2323000000000000−22220000000000002−22−26−66−6000000000000000000
χ5544-4-4-4440000-44-400000000-440000000000000000−2i22i200000000000000−2i22i22i2−2i2000000000000000000
χ5644-4-4-4440000-44-400000000-4400000000000000002i2−2i2000000000000002i2−2i2−2i22i2000000000000000000
χ5744-4-4-44-200002-222323−23−2300002-2−232300000000000000−2i22i20000000000i6−i6−i6i6i2−i2−i2i2000000000000000000
χ5844-4-4-44-200002-222323−23−2300002-2−2323000000000000002i2−2i20000000000−i6i6i6−i6−i2i2i2−i2000000000000000000
χ5944-4-4-44-200002-22−23−23232300002-223−2300000000000000−2i22i20000000000−i6i6i6−i6i2−i2−i2i2000000000000000000
χ6044-4-4-44-200002-22−23−23232300002-223−23000000000000002i2−2i20000000000i6−i6−i6i6−i2i2i2−i2000000000000000000
χ614-44-40044i−4i00-4-440000000000004i−4i00002i−2i02-200000002i−2i2i−2i2-22-200000000000000000000000000
χ624-44-40044i−4i00-4-440000000000004i−4i0000−2i2i0-220000000−2i2i−2i2i-22-2200000000000000000000000000
χ634-44-4004−4i4i00-4-44000000000000−4i4i00002i−2i0-2200000002i−2i2i−2i-22-2200000000000000000000000000
χ644-44-4004−4i4i00-4-44000000000000−4i4i0000−2i2i02-20000000−2i2i−2i2i2-22-200000000000000000000000000
χ654-44-400-24i−4i0022-223−2323−2300000000−2i2i−2i32i3002i−2i02-200000002ζ14−2ζ142ζ22−2ζ22−1+i31−i3−1−i31+i300000000000000000000000000
χ664-44-400-24i−4i0022-223−2323−2300000000−2i2i−2i32i300−2i2i0-220000000−2ζ142ζ14−2ζ222ζ221−i3−1+i31+i3−1−i300000000000000000000000000
χ674-44-400-24i−4i0022-2−2323−232300000000−2i2i2i3−2i3002i−2i02-200000002ζ22−2ζ222ζ14−2ζ14−1−i31+i3−1+i31−i300000000000000000000000000
χ684-44-400-24i−4i0022-2−2323−232300000000−2i2i2i3−2i300−2i2i0-220000000−2ζ222ζ22−2ζ142ζ141+i3−1−i31−i3−1+i300000000000000000000000000
χ694-44-400-2−4i4i0022-223−2323−23000000002i−2i2i3−2i3002i−2i0-2200000002ζ22−2ζ222ζ14−2ζ141+i3−1−i31−i3−1+i300000000000000000000000000
χ704-44-400-2−4i4i0022-223−2323−23000000002i−2i2i3−2i300−2i2i02-20000000−2ζ222ζ22−2ζ142ζ14−1−i31+i3−1+i31−i300000000000000000000000000
χ714-44-400-2−4i4i0022-2−2323−2323000000002i−2i−2i32i3002i−2i0-2200000002ζ14−2ζ142ζ22−2ζ221−i3−1+i31+i3−1−i300000000000000000000000000
χ724-44-400-2−4i4i0022-2−2323−2323000000002i−2i−2i32i300−2i2i02-20000000−2ζ142ζ14−2ζ222ζ22−1+i31−i3−1−i31+i300000000000000000000000000
χ734-4-44004004-44-4-44-4-440000000000000000000000000000000000000000000000000000002i−2i2i−2i00
χ744-4-44004004-44-4-44-4-44000000000000000000000000000000000000000000000000000000−2i2i−2i2i00
χ754-4-4400400-444-4-4-444-40000000000000000000000000000000000000000000000000000002i−2i−2i2i00
χ764-4-4400400-444-4-4-444-4000000000000000000000000000000000000000000000000000000−2i2i2i−2i00
χ778-8-8800-4008-8-444-444-4000000000000000000000000000000000000000000000000000000000000
χ788-8-8800-400-88-4444-4-44000000000000000000000000000000000000000000000000000000000000

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