Finite Group Databasebeta

← Group #11772618

Character table — Group #11772618

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222222222224444444444444444444444448888888888888888888812121212121212121212121224242424242424242424242424242424242472727272
order122222336666666666344444466666666612121212121212121212121212121212121212121212121212121212444412121212121212124488881212121224242424242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1ii−i−i-1-1-1-1iiii−i−i−i−iii−i−i
χ6111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1−i−iii-1-1-1-1−i−i−i−iiiii−i−iii
χ7111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i1111iiii−i−i−i−i−i−iii
χ8111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii1111−i−i−i−iiiiiii−i−i
χ91-11-11-11111-1-1-111-1-1-111-11-11-11-111-1-1-1-1111-1-1-1-1111-1111-1-1-111-1-11111-1-1-1-1ii−i−iiiii−i−i−i−ii−i1-11-1ii−i−i11-1-111-1-1i−ii−i
χ101-11-11-11111-1-1-111-1-1-111-11-11-11-111-1-1-1-1111-1-1-1-1111-1111-1-1-111-1-11111-1-1-1-1ii−i−iiiii−i−i−i−ii−i-11-11ii−i−i-1-111-1-111−ii−ii
χ111-11-11-11111-1-1-111-1-1-111-11-11-11-111-1-1-1-1111-1-1-1-1111-1111-1-1-111-1-11111-1-1-1-1−i−iii−i−i−i−iiiii−ii1-11-1−i−iii11-1-111-1-1−ii−ii
χ121-11-11-11111-1-1-111-1-1-111-11-11-11-111-1-1-1-1111-1-1-1-1111-1111-1-1-111-1-11111-1-1-1-1−i−iii−i−i−i−iiiii−ii-11-11−i−iii-1-111-1-111i−ii−i
χ131-11-11-11111-1-1-111-1-1-111-1-11-111-111-1-1-1-1111-1-111-1-11-1-1-1-111111-1-1-1-1-1-11111ii−i−iiiii−i−i−i−i−iii−i−ii−i−iiiii−i−i−i−iii-111-1
χ141-11-11-11111-1-1-111-1-1-111-1-11-111-111-1-1-1-1111-1-111-1-11-1-1-1-111111-1-1-1-1-1-11111ii−i−iiiii−i−i−i−i−ii−iii−i−i−iii−i−iiiii−i−i1-1-11
χ151-11-11-11111-1-1-111-1-1-111-1-11-111-111-1-1-1-1111-1-111-1-11-1-1-1-111111-1-1-1-1-1-11111−i−iii−i−i−i−iiiiii−ii−i−iiii−i−iii−i−i−i−iii1-1-11
χ161-11-11-11111-1-1-111-1-1-111-1-11-111-111-1-1-1-1111-1-111-1-11-1-1-1-111111-1-1-1-1-1-11111−i−iii−i−i−i−iiiiii−i−iii−iii−i−i−i−iiiii−i−i-111-1
χ172222222222222222222-2-22-2-22222222222-2-2-2-2-2-2-2-2-2-222-222-2-2-2-2-222-2-222-2-20000000000000000000000000000000000
χ182222222222222222222-2-2-222-2222222222-2-2-2-22222-2-2-2-22-2-22-2-2-2-2-2-222-2-2220000000000000000000000000000000000
χ192222222-1222-1-12-1222-1222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-12-122-12-1-1-1-1-1-1-1-1-1-1-1-10000000000000022220000-1-1-1-1-1-1-1-10000
χ202222222-1222-1-12-1222-1222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-12-122-12-1-1-1-1-1-1-1-1-1-1-1-100000000000000-2-2-2-20000111111110000
χ212222222-1222-1-12-1222-122-2-2-2-2-1-1-1-1-1-1-1-1-122221111-1-1-21-2-21-2-1-1-1-111111111000000000000002i2i−2i−2i0000−i−i−i−iiiii0000
χ222222222-1222-1-12-1222-122-2-2-2-2-1-1-1-1-1-1-1-1-122221111-1-1-21-2-21-2-1-1-1-11111111100000000000000−2i−2i2i2i0000iiii−i−i−i−i0000
χ232222222-1222-1-12-1222-1-2-22-2-22-1-1-1-1-1-1-1-1-1-2-2-2-21111112-1-22-1-21111-1-111-1-11100000000000000000000003−33−33−33−30000
χ242222222-1222-1-12-1222-1-2-22-2-22-1-1-1-1-1-1-1-1-1-2-2-2-21111112-1-22-1-21111-1-111-1-1110000000000000000000000−33−33−33−330000
χ252222222-1222-1-12-1222-1-2-2-222-2-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111-212-212111111-1-111-1-10000000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ262222222-1222-1-12-1222-1-2-2-222-2-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111-212-212111111-1-111-1-10000000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ27222222-12-1-1-122-12-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1222222-12-1-12-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1220000-1-1-1-1000000000000
χ28222222-12-1-1-122-12-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1222222-12-1-12-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111-2-200001111000000000000
χ29222222-12-1-1-122-12-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2221-211-21-1-1-1-1111111112222-1-1-1-1-1-1-1-1-2-200001111000000000000
χ30222222-12-1-1-122-12-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2221-211-21-1-1-1-111111111-2-2-2-211111111220000-1-1-1-1000000000000
χ31222222-12-1-1-122-12-1-1-1-1-2-22-2-2222-1-1-1-1-1-1-11111-2-2-2-2-2-2-121-1211111-1-111-1-1110000−i3−i3i3i3−i3−i3i3i3000000−i3i3−i3i3000000000000
χ32222222-12-1-1-122-12-1-1-1-1-2-22-2-2222-1-1-1-1-1-1-11111-2-2-2-2-2-2-121-1211111-1-111-1-1110000i3i3−i3−i3i3i3−i3−i3000000i3−i3i3−i3000000000000
χ33222222-12-1-1-122-12-1-1-1-1-2-2-222-222-1-1-1-1-1-1-111112222-2-21-2-11-2-1111111-1-111-1-10000−i3−i3i3i3−i3−i3i3i3000000i3−i3i3−i3000000000000
χ34222222-12-1-1-122-12-1-1-1-1-2-2-222-222-1-1-1-1-1-1-111112222-2-21-2-11-2-1111111-1-111-1-10000i3i3−i3−i3i3i3−i3−i3000000−i3i3−i3i3000000000000
χ352-22-22-22222-2-2-222-2-2-22-2222-2-22-222-2-2-2-22-2-22222-2-2-2222-2-2-22-2-22222-2-2-2-2220000000000000000000000000000000000
χ362-22-22-22222-2-2-222-2-2-22-22-2-2222-222-2-2-2-22-2-222-2-222-22-2-2222-2-2-222-2-22222-2-20000000000000000000000000000000000
χ372-22-22-22-122-2112-1-2-2-2-12-22-22-2-11-1-11111-122-2-211-1-1-112-12-21-2-1-111-1-1-1-11111000000000000002-22-20000-1-111-1-1110000
χ382-22-22-22-122-2112-1-2-2-2-12-22-22-2-11-1-11111-122-2-211-1-1-112-12-21-2-1-111-1-1-1-1111100000000000000-22-22000011-1-111-1-10000
χ392-22-22-22-122-2112-1-2-2-2-12-2-22-22-11-1-11111-122-2-2-1-111-11-21-22-12-1-1111111-1-1-1-1000000000000002i−2i−2i2i0000−i−iiiii−i−i0000
χ402-22-22-22-122-2112-1-2-2-2-12-2-22-22-11-1-11111-122-2-2-1-111-11-21-22-12-1-1111111-1-1-1-100000000000000−2i2i2i−2i0000ii−i−i−i−iii0000
χ412-22-22-22-122-2112-1-2-2-2-1-2222-2-2-11-1-11111-1-2-222-1-1111-12-1-2-21211-1-1-1-11111-1-100000000000000000000003−3−333−3−330000
χ422-22-22-22-122-2112-1-2-2-2-1-2222-2-2-11-1-11111-1-2-222-1-1111-12-1-2-21211-1-1-1-11111-1-10000000000000000000000−333−3−333−30000
χ432-22-22-22-122-2112-1-2-2-2-1-22-2-222-11-1-11111-1-2-22211-1-11-1-2122-1-211-1-111-1-1-1-1110000000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ442-22-22-22-122-2112-1-2-2-2-1-22-2-222-11-1-11111-1-2-22211-1-11-1-2122-1-211-1-111-1-1-1-1110000000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ452-22-22-2-12-1-11-2-2-12111-12-22-22-22-2-1-11111-1-1-111-2-2222-2-12-11-21-1-111-1-1-1-111112i2i−2i−2i−i−i−i−iiiii2i−2i0000−i−iii000000000000
χ462-22-22-2-12-1-11-2-2-12111-12-22-22-22-2-1-11111-1-1-111-2-2222-2-12-11-21-1-111-1-1-1-11111−2i−2i2i2iiiii−i−i−i−i−2i2i0000ii−i−i000000000000
χ472-22-22-2-12-1-11-2-2-12111-12-2-22-222-2-1-11111-1-1-11122-2-22-21-21-12-1-1-1111111-1-1-1-12i2i−2i−2i−i−i−i−iiiii−2i2i0000ii−i−i000000000000
χ482-22-22-2-12-1-11-2-2-12111-12-2-22-222-2-1-11111-1-1-11122-2-22-21-21-12-1-1-1111111-1-1-1-1−2i−2i2i2iiiii−i−i−i−i2i−2i0000−i−iii000000000000
χ492-22-22-2-12-1-11-2-2-12111-1-2222-2-22-2-1-11111-111-1-122-2-2-22-1211-2-111-1-1-1-11111-1-1000033−3−3−3−3330000003−3−33000000000000
χ502-22-22-2-12-1-11-2-2-12111-1-2222-2-22-2-1-11111-111-1-122-2-2-22-1211-2-111-1-1-1-11111-1-10000−3−33333−3−3000000−333−3000000000000
χ512-22-22-2-12-1-11-2-2-12111-1-22-2-2222-2-1-11111-111-1-1-2-222-221-2-1-12111-1-111-1-1-1-111000033−3−3−3−333000000−333−3000000000000
χ522-22-22-2-12-1-11-2-2-12111-1-22-2-2222-2-1-11111-111-1-1-2-222-221-2-1-12111-1-111-1-1-1-1110000−3−33333−3−30000003−3−33000000000000
χ53444444-2-2-2-2-2-2-2-2-2-2-2-21444444-2-21111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111111110000000000000000000000000000000000
χ54444444-2-2-2-2-2-2-2-2-2-2-2-2144-4-4-4-4-2-21111111-2-2-2-22222-2-22222221111-1-1-1-1-1-1-1-10000000000000000000000000000000000
χ55444444-2-2-2-2-2-2-2-2-2-2-2-21-4-44-4-44-2-211111112222222222-2-22-2-22-1-1-1-111-1-111-1-10000000000000000000000000000000000
χ56444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-444-4-2-211111112222-2-2-2-22222-222-2-1-1-1-1-1-111-1-1110000000000000000000000000000000000
χ574444-4-444-4-444444-4-444000000-4-4-4-444-4-4400000000000000000000000000000000000000000000000000000000000000
χ584444-4-44-2-4-44-2-24-2-4-44-20000002222-2-222-20000−2i32i3−2i32i300000000000000−2i32i300−2i32i30000000000000000000000000000000000
χ594444-4-44-2-4-44-2-24-2-4-44-20000002222-2-222-200002i3−2i32i3−2i3000000000000002i3−2i3002i3−2i30000000000000000000000000000000000
χ604444-4-4-2422-244-2422-2-2000000-4-422-2-222-2−2i32i3−2i32i3000000000000−2i32i3−2i32i3000000000000000000000000000000000000000000
χ614444-4-4-2422-244-2422-2-2000000-4-422-2-222-22i3−2i32i3−2i30000000000002i3−2i32i3−2i3000000000000000000000000000000000000000000
χ624444-4-4-2-222-2-2-2-2-222-2100000022-1-111-1-11−2i32i3−2i32i3−2i32i3−2i32i300000000i3−i3i3−i33-3i3−i33-3i3−i30000000000000000000000000000000000
χ634444-4-4-2-222-2-2-2-2-222-2100000022-1-111-1-11−2i32i3−2i32i32i3−2i32i3−2i300000000i3−i3i3−i3-33−i3i3-33−i3i30000000000000000000000000000000000
χ644444-4-4-2-222-2-2-2-2-222-2100000022-1-111-1-112i3−2i32i3−2i3−2i32i3−2i32i300000000−i3i3−i3i3-33i3−i3-33i3−i30000000000000000000000000000000000
χ654444-4-4-2-222-2-2-2-2-222-2100000022-1-111-1-112i3−2i32i3−2i32i3−2i32i3−2i300000000−i3i3−i3i33-3−i3i33-3−i3i30000000000000000000000000000000000
χ6644-4-400440044-4-4-400-4400000000004-400-400000000000000000000000000002-22-22-22-22-22-20000000000000000000000
χ6744-4-400440044-4-4-400-4400000000004-400-40000000000000000000000000000-22-22-22-22-22-220000000000000000000000
χ6844-4-400-24−2i32i3-24-42-4−2i32i32-200000000−2i32i3-22−2i32i3200000000000000000000000000002-22-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i30000000000000000000000
χ6944-4-400-24−2i32i3-24-42-4−2i32i32-200000000−2i32i3-22−2i32i320000000000000000000000000000-22-221+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i30000000000000000000000
χ7044-4-400-242i3−2i3-24-42-42i3−2i32-2000000002i3−2i3-222i3−2i3200000000000000000000000000002-22-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i30000000000000000000000
χ7144-4-400-242i3−2i3-24-42-42i3−2i32-2000000002i3−2i3-222i3−2i320000000000000000000000000000-22-221−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i30000000000000000000000
χ724-44-44-4-2-2-2-2222-2-222214-44-44-4-2211-1-1-1-11-2-22222-2-2-22-2-2-222211-1-11111-1-1-1-10000000000000000000000000000000000
χ734-44-44-4-2-2-2-2222-2-222214-4-44-44-2211-1-1-1-11-2-222-2-222-22222-2-2-211-1-1-1-1-1-111110000000000000000000000000000000000
χ744-44-44-4-2-2-2-2222-2-22221-4444-4-4-2211-1-1-1-1122-2-2-2-2222-2-2-2222-2-1-11111-1-1-1-1110000000000000000000000000000000000
χ754-44-44-4-2-2-2-2222-2-22221-44-4-444-2211-1-1-1-1122-2-222-2-22-222-2-2-22-1-111-1-11111-1-10000000000000000000000000000000000
χ764-44-4-4444-4-4-4-4-44444-44000000-44-4-4-4-444400000000000000000000000000000000000000000000000000000000000000
χ774-44-4-444-2-4-4-4224-244-4-20000002-22222-2-2-20000−2i32i32i3−2i3000000000000002i3−2i300−2i32i30000000000000000000000000000000000
χ784-44-4-444-2-4-4-4224-244-4-20000002-22222-2-2-200002i3−2i3−2i32i300000000000000−2i32i3002i3−2i30000000000000000000000000000000000
χ794-44-4-44-24222-4-4-24-2-22-2000000-442222-2-2-2−2i32i32i3−2i3000000000000−2i32i32i3−2i3000000000000000000000000000000000000000000
χ804-44-4-44-24222-4-4-24-2-22-2000000-442222-2-2-22i3−2i3−2i32i30000000000002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ814-44-4-44-2-222222-2-2-2-2210000002-2-1-1-1-1111−2i32i32i3−2i3−2i32i32i3−2i300000000i3−i3−i3i3-33−i3i33-3i3−i30000000000000000000000000000000000
χ824-44-4-44-2-222222-2-2-2-2210000002-2-1-1-1-1111−2i32i32i3−2i32i3−2i3−2i32i300000000i3−i3−i3i33-3i3−i3-33−i3i30000000000000000000000000000000000
χ834-44-4-44-2-222222-2-2-2-2210000002-2-1-1-1-11112i3−2i3−2i32i3−2i32i32i3−2i300000000−i3i3i3−i33-3−i3i3-33i3−i30000000000000000000000000000000000
χ844-44-4-44-2-222222-2-2-2-2210000002-2-1-1-1-11112i3−2i3−2i32i32i3−2i3−2i32i300000000−i3i3i3−i3-33i3−i33-3−i3i30000000000000000000000000000000000
χ854-4-44004400-4-44-4-400440000000000-4400-400000000000000000000000000002i−2i−2i2i2i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ864-4-44004400-4-44-4-400440000000000-4400-40000000000000000000000000000−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ874-4-4400-24−2i32i32-442-42i3−2i3-2-200000000−2i32i32-22i3−2i3200000000000000000000000000002i−2i−2i2i2ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ70000000000000000000000
χ884-4-4400-24−2i32i32-442-42i3−2i3-2-200000000−2i32i32-22i3−2i320000000000000000000000000000−2i2i2i−2i−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ70000000000000000000000
χ894-4-4400-242i3−2i32-442-4−2i32i3-2-2000000002i3−2i32-2−2i32i3200000000000000000000000000002i−2i−2i2i2ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ110000000000000000000000
χ904-4-4400-242i3−2i32-442-4−2i32i3-2-2000000002i3−2i32-2−2i32i320000000000000000000000000000−2i2i2i−2i−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ9188-8-8008-4008-44-8400-8-40000000000-4400400000000000000000000000000000000000000000000000000000000000000
χ9288-8-800-4-4−4i34i3-4-4444−4i34i342000000002i3−2i32-22i3−2i3-200000000000000000000000000000000000000000000000000000000000000
χ9388-8-800-4-44i3−4i3-4-44444i3−4i34200000000−2i32i32-2−2i32i3-200000000000000000000000000000000000000000000000000000000000000
χ948-8-88008-400-84-4-84008-400000000004-400400000000000000000000000000000000000000000000000000000000000000
χ958-8-8800-4-4−4i34i344-4444i3−4i3-42000000002i3−2i3-22−2i32i3-200000000000000000000000000000000000000000000000000000000000000
χ968-8-8800-4-44i3−4i344-444−4i34i3-4200000000−2i32i3-222i3−2i3-200000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.