Finite Group Databasebeta

← Group #13168641

Character table — Group #13168641

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size11112222222222222244444444444444444466668888888888888812121212121212121212121212121212121212121818181818181818181818181818242424242424242424242424242424243636363636363636363636108108
order1222333446666666663336666666661212121212124444366612121212121212121212444412121212121212121212121212121212224444666612121212121212121212121212121212121212122446612121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111111111-1-1-1-11-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-11-1-111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-1111111
χ5111111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-11-1-1-1-1-11111-1-1
χ6111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-1-111-1-1-1-111
χ7111111111111111111111111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-111
χ8111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1
χ91111111-1-1111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-111-1-1111111111111111-11-111-1-111-1-111-1-1-1-1-1-1-1-1-111-1-11-1
χ101111111-1-1111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-111-1-1-1-111-1-1-1-111-1-1-1-111111-1-1111-1-111-1-1-1-111-111-1-111-1-111-11
χ111111111-1-1111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-1-111-111-1-1-1-11111-1-111-111-1-1-1-111-11
χ121111111-1-1111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-111-1-1111-11111111-1-11-1
χ131111111-1-1111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-111-1-11-11111111-1-1-11
χ141111111-1-1111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-1-11-1-11111-1-1-1-11111-111-1-1-1-1111-1
χ151111111-1-1111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-111-1-1-111-1-11111-1-1-111-1-111-1-1111-1
χ161111111-1-1111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-11111111111111111-11-11-1-111-1-111-1-111-1-1-1-1-1-1-111-1-1-11
χ17222222-12222-1-12-12222-1-12-1-12-1-12-1-12222-1-12222-1-1-1-122-1-1-1-1-1-1-1-12200-1-1-1-1-1-1-1-1222200000000220000-1-1-1-12200-1-1-1-1-1-1-1-10000200-1-100000000
χ18222222-12222-1-12-12222-1-12-1-12-1-12-1-12222-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-2-200-1-1-1-11111222200000000-2-200001111-2-200-1-1-1-111110000-2001100000000
χ19222222-12222-1-12-12222-1-12-1-12-1-12-1-12222-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-1-1-122001111-1-1-1-1-2-2-2-200000000-2-20000111122001111-1-1-1-10000-2001100000000
χ20222222-12222-1-12-12222-1-12-1-12-1-12-1-12222-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-1-1-1-2-20011111111-2-2-2-200000000220000-1-1-1-1-2-200111111110000200-1-100000000
χ21222222-1-2-222-1-12-12222-1-12-1-12-1-12-1-1-2-2-2-21122-2-2-1-1-1-1-2-2111111112-200-1-111-1-11122-2-200000000220000-1-1-1-12-200-1-111-1-1110000-2001100000000
χ22222222-1-2-222-1-12-12222-1-12-1-12-1-12-1-1-2-2-2-21122-2-2-1-1-1-1-2-211111111-2200-1-11111-1-122-2-200000000-2-200001111-2200-1-11111-1-10000200-1-100000000
χ23222222-1-2-222-1-12-12222-1-12-1-12-1-12-1-1-2-2-2-211-2-222-1-1-1-1-2-2111111112-20011-1-1-1-111-2-22200000000-2-2000011112-20011-1-1-1-1110000200-1-100000000
χ24222222-1-2-222-1-12-12222-1-12-1-12-1-12-1-1-2-2-2-211-2-222-1-1-1-1-2-211111111-220011-1-111-1-1-2-22200000000220000-1-1-1-1-220011-1-111-1-10000-2001100000000
χ2522222-1222-1222-12-122-12-1-12-1-12-1-12-122-1-1222222-1-1-1-1-1-122-1-1-1-1-1-1002222220000-1-1-1-1-1-1-1-1220000-1-1-1-100000022-1-1-1-10000-1-1-1-100200-1-1000000
χ2622222-1222-1222-12-122-12-1-12-1-12-1-12-122-1-1222222-1-1-1-1-1-122-1-1-1-1-1-100-2-222220000-1-1-1-11111-2-200001111000000-2-2-1-1-1-10000111100-20011000000
χ2722222-1222-1222-12-122-12-1-12-1-12-1-12-122-1-122-2-2-2-2-1-1-1-1-1-122-1-1-1-1-1-10022-2-2-2-200001111-1-1-1-1-2-2000011110000002211110000-1-1-1-100-20011000000
χ2822222-1222-1222-12-122-12-1-12-1-12-1-12-122-1-122-2-2-2-2-1-1-1-1-1-122-1-1-1-1-1-100-2-2-2-2-2-2000011111111220000-1-1-1-1000000-2-211110000111100200-1-1000000
χ2922222-12-2-2-1222-12-122-12-1-12-1-12-1-12-1-2-211-2-222-2-2-1-1-1-111-2-2111111002-222-2-20000-1-111-1-111220000-1-1-1-10000002-2-1-1110000-1-11100-20011000000
χ3022222-12-2-2-1222-12-122-12-1-12-1-12-1-12-1-2-211-2-222-2-2-1-1-1-111-2-211111100-2222-2-20000-1-11111-1-1-2-200001111000000-22-1-111000011-1-100200-1-1000000
χ3122222-12-2-2-1222-12-122-12-1-12-1-12-1-12-1-2-211-2-2-2-222-1-1-1-111-2-2111111002-2-2-222000011-1-1-1-111-2-2000011110000002-211-1-10000-1-11100200-1-1000000
χ3222222-12-2-2-1222-12-122-12-1-12-1-12-1-12-1-2-211-2-2-2-222-1-1-1-111-2-211111100-22-2-222000011-1-111-1-1220000-1-1-1-1000000-2211-1-1000011-1-100-20011000000
χ332222-122222-122222-1-1-1-12-1-12-1-12-1-12-1-122220000-1-1-1-1-1-1-1-122-1-1-1-12222000022220000222200220000000000-1-1-1-10000-1-1-1-1-1-1-1-10200000-1-1-1-100
χ342222-122222-122222-1-1-1-12-1-12-1-12-1-12-1-122220000-1-1-1-1-1-1-1-122-1-1-1-122-2-2000022220000-2-2-2-200-2-20000000000-1-1110000-1-1-1-111110-200000111100
χ352222-122222-122222-1-1-1-12-1-12-1-12-1-12-1-122220000-1-1-1-1-1-1-1-122-1-1-1-1-2-2220000-2-2-2-20000222200-2-2000000000011-1-100001111-1-1-1-10-200000111100
χ362222-122222-122222-1-1-1-12-1-12-1-12-1-12-1-122220000-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-20000-2-2-2-20000-2-2-2-20022000000000011110000111111110200000-1-1-1-100
χ372222-122-2-22-122222-1-1-1-12-1-12-1-12-1-1211-2-2-2-20000-1-1-1-11111-2-211112-22-2000022-2-2000022-2-200220000000000-11-110000-1-111-1-1110-200000-1-11100
χ382222-122-2-22-122222-1-1-1-12-1-12-1-12-1-1211-2-2-2-20000-1-1-1-11111-2-211112-2-22000022-2-20000-2-22200-2-20000000000-111-10000-1-11111-1-1020000011-1-100
χ392222-122-2-22-122222-1-1-1-12-1-12-1-12-1-1211-2-2-2-20000-1-1-1-11111-2-21111-222-20000-2-222000022-2-200-2-200000000001-1-11000011-1-1-1-111020000011-1-100
χ402222-122-2-22-122222-1-1-1-12-1-12-1-12-1-1211-2-2-2-20000-1-1-1-11111-2-21111-22-220000-2-2220000-2-222002200000000001-11-1000011-1-111-1-10-200000-1-11100
χ412-22-222200-2-22-2-2-222-2222-22-2-2-2-22-22000000000022-2-20000000000000000000000000000002-22i−2i2i−2i22-2-22i2i−2i−2i000000000000000000000002i−2i0000
χ422-22-222200-2-22-2-2-222-2222-22-2-2-2-22-22000000000022-2-20000000000000000000000000000002-2−2i2i−2i2i22-2-2−2i−2i2i2i00000000000000000000000−2i2i0000
χ432-22-222200-2-22-2-2-222-2222-22-2-2-2-22-22000000000022-2-2000000000000000000000000000000-222i−2i−2i2i-2-222−2i−2i2i2i000000000000000000000002i−2i0000
χ442-22-222200-2-22-2-2-222-2222-22-2-2-2-22-22000000000022-2-2000000000000000000000000000000-22−2i2i2i−2i-2-2222i2i−2i−2i00000000000000000000000−2i2i0000
χ452-2-222222-2-22-2-222-2-2-2222-2-2-2222-2-2-22-22-22-22i−2i2i−2i2-2-222-22-22-222-2-200002i−2i2i−2i00002i−2i2i−2i00000000000000000000002i−2i2i−2i000000000000000000000
χ462-2-222222-2-22-2-222-2-2-2222-2-2-2222-2-2-22-22-22-2−2i2i−2i2i2-2-222-22-22-222-2-20000−2i2i−2i2i0000−2i2i−2i2i0000000000000000000000−2i2i−2i2i000000000000000000000
χ472-2-22222-22-22-2-222-2-2-2222-2-2-2222-2-2-2-22-22-222i−2i−2i2i2-2-22-22-22-22-2-22200002i−2i−2i2i00002i−2i−2i2i00000000000000000000002i−2i−2i2i000000000000000000000
χ482-2-22222-22-22-2-222-2-2-2222-2-2-2222-2-2-2-22-22-22−2i2i2i−2i2-2-22-22-22-22-2-2220000−2i2i2i−2i0000−2i2i2i−2i0000000000000000000000−2i2i2i−2i000000000000000000000
χ492-2-2222-12-2-22112-1-2-2-22-1-1-2112-1-1-2112-22-2-112i−2i2i−2i-111-12-2-11-11-1-1110000−ii−ii3−33−32i−2i2i−2i00000000000000−i3i3−i3i30000−ii−ii3−33−30000000−i3i300000000
χ502-2-2222-12-2-22112-1-2-2-22-1-1-2112-1-1-2112-22-2-112i−2i2i−2i-111-12-2-11-11-1-1110000−ii−ii−33−332i−2i2i−2i00000000000000i3−i3i3−i30000−ii−ii−33−330000000i3−i300000000
χ512-2-2222-12-2-22112-1-2-2-22-1-1-2112-1-1-2112-22-2-11−2i2i−2i2i-111-12-2-11-11-1-1110000i−ii−i3−33−3−2i2i−2i2i00000000000000i3−i3i3−i30000i−ii−i3−33−30000000i3−i300000000
χ522-2-2222-12-2-22112-1-2-2-22-1-1-2112-1-1-2112-22-2-11−2i2i−2i2i-111-12-2-11-11-1-1110000i−ii−i−33−33−2i2i−2i2i00000000000000−i3i3−i3i30000i−ii−i−33−330000000−i3i300000000
χ532-2-2222-1-22-22112-1-2-2-22-1-1-2112-1-1-211-22-221-12i−2i−2i2i-111-1-221-11-111-1-10000−iii−i3−3−332i−2i−2i2i00000000000000−i3i3−i3i30000−iii−i3−3−330000000i3−i300000000
χ542-2-2222-1-22-22112-1-2-2-22-1-1-2112-1-1-211-22-221-12i−2i−2i2i-111-1-221-11-111-1-10000−iii−i−333−32i−2i−2i2i00000000000000i3−i3i3−i30000−iii−i−333−30000000−i3i300000000
χ552-2-2222-1-22-22112-1-2-2-22-1-1-2112-1-1-211-22-221-1−2i2i2i−2i-111-1-221-11-111-1-10000i−i−ii3−3−33−2i2i2i−2i00000000000000i3−i3i3−i30000i−i−ii3−3−330000000−i3i300000000
χ562-2-2222-1-22-22112-1-2-2-22-1-1-2112-1-1-211-22-221-1−2i2i2i−2i-111-1-221-11-111-1-10000i−i−ii−333−3−2i2i2i−2i00000000000000−i3i3−i3i30000i−i−ii−333−30000000i3−i300000000
χ572-2-222-122-212-2-2-121-2-2-12-11-21-12-11-212-2-112-22i−2i2i−2i-111-1-112-2-11-1-11100002i−2i2i−2i0000−ii−ii3−33−3000000−i3i3−i3i300000000−ii−ii00003−33−300000−i3i3000000
χ582-2-222-122-212-2-2-121-2-2-12-11-21-12-11-212-2-112-22i−2i2i−2i-111-1-112-2-11-1-11100002i−2i2i−2i0000−ii−ii−33−33000000i3−i3i3−i300000000−ii−ii0000−33−3300000i3−i3000000
χ592-2-222-122-212-2-2-121-2-2-12-11-21-12-11-212-2-112-2−2i2i−2i2i-111-1-112-2-11-1-1110000−2i2i−2i2i0000i−ii−i3−33−3000000i3−i3i3−i300000000i−ii−i00003−33−300000i3−i3000000
χ602-2-222-122-212-2-2-121-2-2-12-11-21-12-11-212-2-112-2−2i2i−2i2i-111-1-112-2-11-1-1110000−2i2i−2i2i0000i−ii−i−33−33000000−i3i3−i3i300000000i−ii−i0000−33−3300000−i3i3000000
χ612-2-222-12-2212-2-2-121-2-2-12-11-21-12-11-21-221-1-222i−2i−2i2i-111-11-1-221-111-1-100002i−2i−2i2i0000−iii−i3−3−33000000−i3i3−i3i300000000−iii−i00003−3−3300000i3−i3000000
χ622-2-222-12-2212-2-2-121-2-2-12-11-21-12-11-21-221-1-222i−2i−2i2i-111-11-1-221-111-1-100002i−2i−2i2i0000−iii−i−333−3000000i3−i3i3−i300000000−iii−i0000−333−300000−i3i3000000
χ632-2-222-12-2212-2-2-121-2-2-12-11-21-12-11-21-221-1-22−2i2i2i−2i-111-11-1-221-111-1-10000−2i2i2i−2i0000i−i−ii3−3−33000000i3−i3i3−i300000000i−i−ii00003−3−3300000−i3i3000000
χ642-2-222-12-2212-2-2-121-2-2-12-11-21-12-11-21-221-1-22−2i2i2i−2i-111-11-1-221-111-1-10000−2i2i2i−2i0000i−i−ii−333−3000000−i3i3−i3i300000000i−i−ii0000−333−300000i3−i3000000
χ6544444-2-244-24-2-2-2-2-244-2-21-2-21-2-21-2-2144-2-2-2-244441111-2-2-2-21111110000-2-2-2-20000-2-2-2-200000000000000000000001111000000000000000000000
χ6644444-2-244-24-2-2-2-2-244-2-21-2-21-2-21-2-2144-2-2-2-2-4-4-4-41111-2-2-2-211111100002222000022220000000000000000000000-1-1-1-1000000000000000000000
χ6744444-2-2-4-4-24-2-2-2-2-244-2-21-2-21-2-21-2-21-4-4222244-4-411112222-1-1-1-1-1-10000-2-2220000-2-222000000000000000000000011-1-1000000000000000000000
χ6844444-2-2-4-4-24-2-2-2-2-244-2-21-2-21-2-21-2-21-4-42222-4-44411112222-1-1-1-1-1-1000022-2-2000022-2-20000000000000000000000-1-111000000000000000000000
χ694444-24-2444-2-2-24-24-2-2-21-2-21-2-21-2-21-2-2-244-2-200001111-2-211-2-2111144000000-2-2-2-20000000000000000000000-2-2000000111100000000000000000
χ704444-24-2444-2-2-24-24-2-2-21-2-21-2-21-2-21-2-2-244-2-200001111-2-211-2-21111-4-40000002222000000000000000000000022000000-1-1-1-100000000000000000
χ714444-24-2-4-44-2-2-24-24-2-2-21-2-21-2-21-2-21-222-4-4220000111122-1-122-1-1-1-14-4000000-2-2220000000000000000000000-2200000011-1-100000000000000000
χ724444-24-2-4-44-2-2-24-24-2-2-21-2-21-2-21-2-21-222-4-4220000111122-1-122-1-1-1-1-4400000022-2-200000000000000000000002-2000000-1-11100000000000000000
χ734444-2-2444-2-244-24-2-2-21-2-21-2-21-2-21-2-2-2-2-2-2440000111111-2-2-2-211110044000000000000-2-2-2-20000000000000000-2-20000000011110000000000000
χ744444-2-2444-2-244-24-2-2-21-2-21-2-21-2-21-2-2-2-2-2-2440000111111-2-2-2-2111100-4-4000000000000222200000000000000002200000000-1-1-1-10000000000000
χ754444-2-24-4-4-2-244-24-2-2-21-2-21-2-21-2-21-2-22222-4-400001111-1-12222-1-1-1-1004-4000000000000-2-2220000000000000000-220000000011-1-10000000000000
χ764444-2-24-4-4-2-244-24-2-2-21-2-21-2-21-2-21-2-22222-4-400001111-1-12222-1-1-1-100-4400000000000022-2-200000000000000002-200000000-1-1110000000000000
χ7744-4-4444004-4-44-4-4-4-444444-44-4-4-4-44-400000000004-44-40000000000000000000000000000000000000000000000000000000000000000000000000
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Here i is the imaginary unit (i² = −1).