Finite Group Databasebeta

← Group #11785770

Character table — Group #11785770

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size11111111222222222222222222224444444444444444444444444444444444444444444444444444444444441212121212121212181818182424242424242424242424242424242424242424363636363636
order1222222233444466666666666666366666668888121212121212121212121212121212122424242424242424242424242424242424242424242424242424242424242424444444442222444412121212121212121212121212121212448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111
χ7111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ911-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1111-1-1-1-11ii−i−i1111-1-11111-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i11-1-111-1-111-1-1i−ii−i11-1-1ii−i−i11-1-1ii−i−i1-1ii−i−i
χ1011-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1111-1-1-1-11ii−i−i1111-1-11111-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i11-1-1-1-111-1-111i−i−ii11-1-1ii−i−i-1-111−i−iii-11−i−iii
χ1111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1111-1-1-1-11ii−i−i1111-1-11111-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-11111-1-1-1-111−iii−i-1-111−i−iii11-1-1ii−i−i-11−i−iii
χ1211-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1111-1-1-1-11ii−i−i1111-1-11111-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-111-1-11111-1-1−ii−ii-1-111−i−iii-1-111−i−iii1-1ii−i−i
χ1311-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1111-1-1-1-11−i−iii1111-1-11111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii11-1-111-1-111-1-1−ii−ii11-1-1−i−iii11-1-1−i−iii1-1−i−iii
χ1411-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1111-1-1-1-11−i−iii1111-1-11111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii11-1-1-1-111-1-111−iii−i11-1-1−i−iii-1-111ii−i−i-11ii−i−i
χ1511-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1111-1-1-1-11−i−iii1111-1-11111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-1-11111-1-1-1-111i−i−ii-1-111ii−i−i11-1-1−i−iii-11ii−i−i
χ1611-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1111-1-1-1-11−i−iii1111-1-11111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii-1-111-1-11111-1-1i−ii−i-1-111ii−i−i-1-111ii−i−i1-1−i−iii
χ172222222222-2-2-2-222222222222222222222220000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000222200000000000000000000-2-20000
χ182222222222-2-2-2-222222222222222222222220000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-2-2-200000000000000000000220000
χ19222222222-122222-1222-1-1-12-12-12-1-1-1-1-1-1-1-1-1222222-1-12-1-1-1-1-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000022220000002200000000-1-1-1-1-1-1-1-1000000
χ20222222222-122222-1222-1-1-12-12-12-1-1-1-1-1-1-1-1-1222222-1-12-1-1-1-1-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2000000-2-20000000011111111000000
χ21222222222-122222-1222-1-1-12-12-12-1-1-1-1-1-1-1-1-1-2-2-2-222-1-12-1-1-1-1-1-1-12-1-1-1-2-2-2-2111111111111-2-2-2-211111111111100002222000000-2-200000000-1-1-1-11111000000
χ22222222222-122222-1222-1-1-12-12-12-1-1-1-1-1-1-1-1-1-2-2-2-222-1-12-1-1-1-1-1-1-12-1-1-1-2-2-2-2111111111111-2-2-2-21111111111110000-2-2-2-200000022000000001111-1-1-1-1000000
χ2322222222-122222-12-1-1-1222-12-12-12-1-1-1-1-1-1-1-12222-1-122-12-1-1-1-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222000000002200-1-1-1-1-1-1-1-100000000000000
χ2422222222-122222-12-1-1-1222-12-12-12-1-1-1-1-1-1-1-12222-1-122-12-1-1-1-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-200000000-2-2001111111100000000000000
χ2522222222-122222-12-1-1-1222-12-12-12-1-1-1-1-1-1-1-1-2-2-2-2-1-122-12-1-1-1-1-1-1-12-1-11111-2-2-2-2111111111111-2-2-2-211111111222200000000-2-200-1-1-1-1111100000000000000
χ2622222222-122222-12-1-1-1222-12-12-12-1-1-1-1-1-1-1-1-2-2-2-2-1-122-12-1-1-1-1-1-1-12-1-11111-2-2-2-2111111111111-2-2-2-211111111-2-2-2-20000000022001111-1-1-1-100000000000000
χ2722-2-2-2-22222-2-22222-2-2-2-2-2-22222-2-2222-2-2-2-220000-2-2-2-222-2-2-2-2222222000000000000000000000000000000000000000022-2-200000000000000000000-220000
χ2822-2-2-2-22222-2-22222-2-2-2-2-2-22222-2-2222-2-2-2-220000-2-2-2-222-2-2-2-22222220000000000000000000000000000000000000000-2-222000000000000000000002-20000
χ2922-2-2-2-2222-122-2-22-1-2-2-21112-12-1-21-1-1-11111-12i2i−2i−2i22-1-1-21-1-1-1-111-21112i2i2i2i−i−i−i−i−i−i−i−i−i−i−i−i−2i−2i−2i−2iiiiiiiiiiiii000022-2-20000002i−2i00000000-1-111−i−iii000000
χ3022-2-2-2-2222-122-2-22-1-2-2-21112-12-1-21-1-1-11111-12i2i−2i−2i22-1-1-21-1-1-1-111-21112i2i2i2i−i−i−i−i−i−i−i−i−i−i−i−i−2i−2i−2i−2iiiiiiiiiiiii0000-2-222000000−2i2i0000000011-1-1ii−i−i000000
χ3122-2-2-2-2222-122-2-22-1-2-2-21112-12-1-21-1-1-11111-1−2i−2i2i2i22-1-1-21-1-1-1-111-2111−2i−2i−2i−2iiiiiiiiiiiii2i2i2i2i−i−i−i−i−i−i−i−i−i−i−i−i000022-2-2000000−2i2i00000000-1-111ii−i−i000000
χ3222-2-2-2-2222-122-2-22-1-2-2-21112-12-1-21-1-1-11111-1−2i−2i2i2i22-1-1-21-1-1-1-111-2111−2i−2i−2i−2iiiiiiiiiiiii2i2i2i2i−i−i−i−i−i−i−i−i−i−i−i−i0000-2-2220000002i−2i0000000011-1-1−i−iii000000
χ3322-2-2-2-222-1222-2-2-12111-2-2-2-12-121-2-1-1-11111-12i2i−2i−2i-1-1221-2-1-1-1-1111-211−i−i−i−i2i2i2i2i−i−i−i−i−i−i−i−iiiii−2i−2i−2i−2iiiiiiiii22-2-2000000002i−2i00-1-111−i−iii00000000000000
χ3422-2-2-2-222-1222-2-2-12111-2-2-2-12-121-2-1-1-11111-12i2i−2i−2i-1-1221-2-1-1-1-1111-211−i−i−i−i2i2i2i2i−i−i−i−i−i−i−i−iiiii−2i−2i−2i−2iiiiiiiii-2-22200000000−2i2i0011-1-1ii−i−i00000000000000
χ3522-2-2-2-222-1222-2-2-12111-2-2-2-12-121-2-1-1-11111-1−2i−2i2i2i-1-1221-2-1-1-1-1111-211iiii−2i−2i−2i−2iiiiiiiii−i−i−i−i2i2i2i2i−i−i−i−i−i−i−i−i22-2-200000000−2i2i00-1-111ii−i−i00000000000000
χ3622-2-2-2-222-1222-2-2-12111-2-2-2-12-121-2-1-1-11111-1−2i−2i2i2i-1-1221-2-1-1-1-1111-211iiii−2i−2i−2i−2iiiiiiiii−i−i−i−i2i2i2i2i−i−i−i−i−i−i−i−i-2-222000000002i−2i0011-1-1−i−iii00000000000000
χ372-222-2-2-22220000-2-222-222-2-2-222-2-222-222-2-2-2−i2i2−i2i20000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2000000002-22-20000000000000000000000−i2i2−i2i2
χ382-222-2-2-22220000-2-222-222-2-2-222-2-222-222-2-2-2−i2i2−i2i20000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i200000000-22-220000000000000000000000i2−i2i2−i2
χ392-222-2-2-22220000-2-222-222-2-2-222-2-222-222-2-2-2i2−i2i2−i20000000000000000i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2000000002-22-20000000000000000000000i2−i2i2−i2
χ402-222-2-2-22220000-2-222-222-2-2-222-2-222-222-2-2-2i2−i2i2−i20000000000000000i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i200000000-22-220000000000000000000000−i2i2−i2i2
χ412-22-22-22-2222-22-2-2-22-222-2-222-2-2-222-2-22-22-2200002-22-2-2-222-2-2-2-22222000000000000000000000000000000002i−2i2i−2i0000000000002i−2i2i−2i000000000000000000
χ422-22-22-22-2222-22-2-2-22-222-2-222-2-2-222-2-22-22-2200002-22-2-2-222-2-2-2-2222200000000000000000000000000000000−2i2i−2i2i000000000000−2i2i−2i2i000000000000000000
χ432-22-22-22-222-22-22-2-22-222-2-222-2-2-222-2-22-22-220000-22-2222-2-22222-2-2-2-20000000000000000000000000000000000002i−2i2i−2i00000000000000002i−2i2i−2i0000000000
χ442-22-22-22-222-22-22-2-22-222-2-222-2-2-222-2-22-22-220000-22-2222-2-22222-2-2-2-2000000000000000000000000000000000000−2i2i−2i2i0000000000000000−2i2i−2i2i0000000000
χ452-22-22-22-22-1-22-22-212-22-1112-1-21-2-1-111-11-11-10000-221-12-111-1-1-1-1-211100003−33−333−3−333−3−300003−33−333−3−333−3−300002i−2i2i−2i0000000000000000−ii−ii−i3i3−i3i3000000
χ462-22-22-22-22-1-22-22-212-22-1112-1-21-2-1-111-11-11-10000-221-12-111-1-1-1-1-211100003−33−333−3−333−3−300003−33−333−3−333−3−30000−2i2i−2i2i0000000000000000i−ii−ii3−i3i3−i3000000
χ472-22-22-22-22-1-22-22-212-22-1112-1-21-2-1-111-11-11-10000-221-12-111-1-1-1-1-21110000−33−33−3−333−3−3330000−33−33−3−333−3−33300002i−2i2i−2i0000000000000000−ii−iii3−i3i3−i3000000
χ482-22-22-22-22-1-22-22-212-22-1112-1-21-2-1-111-11-11-10000-221-12-111-1-1-1-1-21110000−33−33−3−333−3−3330000−33−33−3−333−3−3330000−2i2i−2i2i0000000000000000i−ii−i−i3i3−i3i3000000
χ492-22-22-22-2-122-22-21-2-11-12-2-2-121-212-111-11-11-10000-112-21-2-1-11111-12-1-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i32i−2i2i−2i000000000000−ii−ii3−33−300000000000000
χ502-22-22-22-2-122-22-21-2-11-12-2-2-121-212-111-11-11-10000-112-21-2-1-11111-12-1-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i3−2i2i−2i2i000000000000i−ii−i−33−3300000000000000
χ512-22-22-22-2-122-22-21-2-11-12-2-2-121-212-111-11-11-10000-112-21-2-1-11111-12-1-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i32i−2i2i−2i000000000000−ii−ii−33−3300000000000000
χ522-22-22-22-2-122-22-21-2-11-12-2-2-121-212-111-11-11-10000-112-21-2-1-11111-12-1-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i3−2i2i−2i2i000000000000i−ii−i3−33−300000000000000
χ532-2-22-222-2222-2-22-2-2-22-2-22222-2-22-22-2-2-22-22200002-22-22222-2-222-2-2-2-2000000000000000000000000000000002i−2i−2i2i0000000000002i−2i−2i2i000000000000000000
χ542-2-22-222-2222-2-22-2-2-22-2-22222-2-22-22-2-2-22-22200002-22-22222-2-222-2-2-2-200000000000000000000000000000000−2i2i2i−2i000000000000−2i2i2i−2i000000000000000000
χ552-2-22-222-222-222-2-2-2-22-2-22222-2-22-22-2-2-22-2220000-22-22-2-2-2-222-2-222220000000000000000000000000000000000002i−2i−2i2i00000000000000002i−2i−2i2i0000000000
χ562-2-22-222-222-222-2-2-2-22-2-22222-2-22-22-2-2-22-2220000-22-22-2-2-2-222-2-22222000000000000000000000000000000000000−2i2i2i−2i0000000000000000−2i2i2i−2i0000000000
χ572-2-22-222-22-1-222-2-21-22-21-1-12-1-2121-1111-11-1-10000-221-1-2111-1-1112-1-1-10000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i30000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i300002i−2i−2i2i0000000000000000−iii−i−333−3000000
χ582-2-22-222-22-1-222-2-21-22-21-1-12-1-2121-1111-11-1-10000-221-1-2111-1-1112-1-1-10000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i30000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i30000−2i2i2i−2i0000000000000000i−i−ii3−3−33000000
χ592-2-22-222-22-1-222-2-21-22-21-1-12-1-2121-1111-11-1-10000-221-1-2111-1-1112-1-1-10000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i30000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i300002i−2i−2i2i0000000000000000−iii−i3−3−33000000
χ602-2-22-222-22-1-222-2-21-22-21-1-12-1-2121-1111-11-1-10000-221-1-2111-1-1112-1-1-10000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i30000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i30000−2i2i2i−2i0000000000000000i−i−ii−333−3000000
χ612-2-22-222-2-122-2-221-21-11-222-121-2-1-2-1111-11-1-10000-112-2-12-1-111-1-11-2113−33−300003−33−33−33−3−33−330000−33−33−33−332i−2i−2i2i000000000000−iii−ii3−i3−i3i300000000000000
χ622-2-22-222-2-122-2-221-21-11-222-121-2-1-2-1111-11-1-10000-112-2-12-1-111-1-11-2113−33−300003−33−33−33−3−33−330000−33−33−33−33−2i2i2i−2i000000000000i−i−ii−i3i3i3−i300000000000000
χ632-2-22-222-2-122-2-221-21-11-222-121-2-1-2-1111-11-1-10000-112-2-12-1-111-1-11-211−33−330000−33−33−33−333−33−300003−33−33−33−32i−2i−2i2i000000000000−iii−i−i3i3i3−i300000000000000
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χ1264-4-4-444-44-2-200002222-222-222-2-2-2-211-1-1-111-1−222222−22000000−3i3i3i−3i−3i3i003i−3i22−2−222−2−2−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−2−222−2−222ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ2300000000000000000000000000000000000000

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