Finite Group Databasebeta

← Group #10714476

Character table — Group #10714476

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888888888888888888888888888884848484848484848
order12222234444666121212126688881212242424242424242424668812121616161616161616242424244848484848484848484848484848484844448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ922222222222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-22200000000-2-2-2-2000000000000000000000000
χ1022222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222-2-2000000002222000000000000000000000000
χ112222222-2-2-2-2222-2-2-2-2220000-2-2000000002-22200-2-2−i2−i2i2i2−i2−i2i2i20000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200000000
χ122222222-2-2-2-2222-2-2-2-2220000-2-2000000002-22200-2-2i2i2−i2−i2i2i2−i2−i20000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200000000
χ132222222-2-2-2-2222-2-2-2-2220000-2-200000000-22-2-20022−i2−i2i2i2i2i2−i2−i20000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200000000
χ142222222-2-2-2-2222-2-2-2-2220000-2-200000000-22-2-20022i2i2−i2−i2−i2−i2i2i20000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200000000
χ15222222-12222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ16222222-12222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111100000000
χ17222222-12222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-211-2-2112222-2-2-2-21111-1-1-1-1-1-1-1-11111111100000000
χ18222222-12222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-211-2-211-2-2-2-22222111111111111-1-1-1-1-1-1-1-100000000
χ19222222-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-1-1-2-2-1-100000000111133−3−333−3−333−3−333−3−300000000
χ20222222-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-1-1-2-2-1-1000000001111−3−333−3−333−3−333−3−33300000000
χ21222222-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-211221100000000-1-1-1-133−3−333−3−3−3−333−3−33300000000
χ22222222-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-211221100000000-1-1-1-1−3−333−3−33333−3−333−3−300000000
χ23222222-1-2-2-2-2-1-1-11111-1-100001133−3−333−3−32-2-1-10011−i2−i2i2i2−i2−i2i2i233−3−3ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ2300000000
χ24222222-1-2-2-2-2-1-1-11111-1-100001133−3−333−3−32-2-1-10011i2i2−i2−i2i2i2−i2−i233−3−3−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ2300000000
χ25222222-1-2-2-2-2-1-1-11111-1-100001133−3−333−3−3-221100-1-1−i2−i2i2i2i2i2−i2−i2−3−333ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ2300000000
χ26222222-1-2-2-2-2-1-1-11111-1-100001133−3−333−3−3-221100-1-1i2i2−i2−i2−i2−i2i2i2−3−333−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ2300000000
χ27222222-1-2-2-2-2-1-1-11111-1-1000011−3−333−3−3332-2-1-10011−i2−i2i2i2−i2−i2i2i2−3−333ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ700000000
χ28222222-1-2-2-2-2-1-1-11111-1-1000011−3−333−3−3332-2-1-10011i2i2−i2−i2i2i2−i2−i2−3−333−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ700000000
χ29222222-1-2-2-2-2-1-1-11111-1-1000011−3−333−3−333-221100-1-1−i2−i2i2i2i2i2−i2−i233−3−3ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ700000000
χ30222222-1-2-2-2-2-1-1-11111-1-1000011−3−333−3−333-221100-1-1i2i2−i2−i2−i2−i2i2i233−3−3−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ700000000
χ312222-2-2222-2-22222222-2-22-22-2-2-22-22-22-22-20000000000000000000000000000000000000000002i−2i
χ322222-2-2222-2-22222222-2-22-22-2-2-22-22-22-22-2000000000000000000000000000000000000000000−2i2i
χ332222-2-2222-2-22222222-2-2-22-22-2-2-22-22-22-2200000000000000000000000000000000000000002i−2i00
χ342222-2-2222-2-22222222-2-2-22-22-2-2-22-22-22-220000000000000000000000000000000000000000−2i2i00
χ352-2-222-222-22-2-2-2222-2-22-200002-20000000000002i−2i002−22−2−i2i2−i2i22i−2i2i−2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i200000000
χ362-2-222-222-22-2-2-2222-2-22-200002-20000000000002i−2i00−22−22i2−i2i2−i22i−2i2i−2i−22−22−22−22i2−i2i2−i2i2−i2i2−i200000000
χ372-2-222-222-22-2-2-2222-2-22-200002-2000000000000−2i2i002−22−2i2−i2i2−i2−2i2i−2i2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000
χ382-2-222-222-22-2-2-2222-2-22-200002-2000000000000−2i2i00−22−22−i2i2−i2i2−2i2i−2i2i−22−22−22−22−i2i2−i2i2−i2i2−i2i200000000
χ392-2-222-22-22-22-2-22-2-2222-222-2-2-222222-2-2-2-2000000002i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ402-2-222-22-22-22-2-22-2-2222-222-2-2-222222-2-2-2-200000000−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ412-2-222-22-22-22-2-22-2-2222-2-2-222-22-2-2-2-222220000000000002-2-220000000000002-22-2-22-2200000000
χ422-2-222-22-22-22-2-22-2-2222-2-2-222-22-2-2-2-22222000000000000-222-2000000000000-22-222-22-200000000
χ432-2-222-2-12-22-211-1-1-111-110000-1133−3−3−3−33300−i3i32i−2i−i3i32−22−2−i2i2−i2i2−ii−iiζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ442-2-222-2-12-22-211-1-1-111-110000-1133−3−3−3−33300−i3i32i−2i−i3i3−22−22i2−i2i2−i2−ii−ii−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ452-2-222-2-12-22-211-1-1-111-110000-1133−3−3−3−33300i3−i3−2i2ii3−i32−22−2i2−i2i2−i2i−ii−iζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ462-2-222-2-12-22-211-1-1-111-110000-1133−3−3−3−33300i3−i3−2i2ii3−i3−22−22−i2i2−i2i2i−ii−i−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ472-2-222-2-12-22-211-1-1-111-110000-11−3−33333−3−300−i3i3−2i2i−i3i32−22−2i2−i2i2−i2i−ii−iζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ482-2-222-2-12-22-211-1-1-111-110000-11−3−33333−3−300−i3i3−2i2i−i3i3−22−22−i2i2−i2i2i−ii−i−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ492-2-222-2-12-22-211-1-1-111-110000-11−3−33333−3−300i3−i32i−2ii3−i32−22−2−i2i2−i2i2−ii−iiζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ502-2-222-2-12-22-211-1-1-111-110000-11−3−33333−3−300i3−i32i−2ii3−i3−22−22i2−i2i2−i2−ii−ii−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ512-2-222-2-1-22-2211-111-1-1-1122-2-21-1-1-1-1-1111100−i3i300i3−i32i−2i−2i2i0000−i3i3i3−i3−ii−iii−ii−i3−3−33−333−300000000
χ522-2-222-2-1-22-2211-111-1-1-1122-2-21-1-1-1-1-1111100−i3i300i3−i3−2i2i2i−2i0000−i3i3i3−i3i−ii−i−ii−ii−333−33−3−3300000000
χ532-2-222-2-1-22-2211-111-1-1-1122-2-21-1-1-1-1-1111100i3−i300−i3i32i−2i−2i2i0000i3−i3−i3i3−ii−iii−ii−i−333−33−3−3300000000
χ542-2-222-2-1-22-2211-111-1-1-1122-2-21-1-1-1-1-1111100i3−i300−i3i3−2i2i2i−2i0000i3−i3−i3i3i−ii−i−ii−ii3−3−33−333−300000000
χ552-2-222-2-1-22-2211-111-1-1-11-2-2221-11111-1-1-1-100−i3i300i3−i300002-2-22i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3-11-111-11-100000000
χ562-2-222-2-1-22-2211-111-1-1-11-2-2221-11111-1-1-1-100−i3i300i3−i30000-222-2i3−i3−i3i3i3−i3−i3i3−i3i3i3−i31-11-1-11-1100000000
χ572-2-222-2-1-22-2211-111-1-1-11-2-2221-11111-1-1-1-100i3−i300−i3i300002-2-22−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3-11-111-11-100000000
χ582-2-222-2-1-22-2211-111-1-1-11-2-2221-11111-1-1-1-100i3−i300−i3i30000-222-2−i3i3i3−i3−i3i3i3−i3i3−i3−i3i31-11-1-11-1100000000
χ592-2-22-222-222-2-2-22-2-222-222-2-222-22-22-2-22-22000000000000000000000000000000000000002-20000
χ602-2-22-222-222-2-2-22-2-222-222-2-222-22-22-2-22-2200000000000000000000000000000000000000-220000
χ612-2-22-222-222-2-2-22-2-222-22-222-22-2-22-222-22-20000000000000000000000000000000000002-2000000
χ622-2-22-222-222-2-2-22-2-222-22-222-22-2-22-222-22-2000000000000000000000000000000000000-22000000
χ634444-4-44-4-444444-4-4-4-4-4-40000440000000000000000000000000000000000000000000000000000
χ644444-4-4-244-4-4-2-2-2-2-2-2-2224-44-422-22-22-22-2200000000000000000000000000000000000000000000
χ654444-4-4-244-4-4-2-2-2-2-2-2-222-44-44222-22-22-22-200000000000000000000000000000000000000000000
χ664444-4-4-2-4-444-2-2-22222220000-2-223−23−232323−23−232300000000000000000000000000000000000000000000
χ674444-4-4-2-4-444-2-2-22222220000-2-2−232323−23−232323−2300000000000000000000000000000000000000000000
χ684-4-44-4444-4-44-4-4444-4-4-440000-440000000000000000000000000000000000000000000000000000
χ694-4-44-44-24-4-4422-2-2-2222-200002-223−23−2323−232323−2300000000000000000000000000000000000000000000
χ704-4-44-44-24-4-4422-2-2-2222-200002-2−232323−2323−23−232300000000000000000000000000000000000000000000
χ714-4-44-44-2-444-422-222-2-22-24-4-44-22-22-222-22-200000000000000000000000000000000000000000000
χ724-4-44-44-2-444-422-222-2-22-2-444-4-222-22-2-22-2200000000000000000000000000000000000000000000
χ7388-8-800800008-8-80000000000000000000000000000000000000000000000000000000000000000
χ7488-8-800-40000-44443−4343−43000000000000000000000000000000000000000000000000000000000000
χ7588-8-800-40000-444−4343−4343000000000000000000000000000000000000000000000000000000000000
χ768-88-80080000-88-80000000000000000000000000000000000000000000000000000000000000000
χ778-88-800-400004-4443−43−4343000000000000000000000000000000000000000000000000000000000000
χ788-88-800-400004-44−434343−43000000000000000000000000000000000000000000000000000000000000

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