Finite Group Databasebeta

← Group #13166830

Character table — Group #13166830

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size112444448888121212121212161818242424242424243636364872112444448888121212121212161818242424242424243636364872112444448888121212121212161818242424242424243636364872
order124233666612122224666244668122424444128361263366661212666126666121266241224241212121224361263366661212666126666121266241224241212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111-111-11-1-11-1-1-1-1111111111111111111111-111-11-1-11-1-1-1-1111111111111111111111-111-11-1-11-1-1-1-1
χ3111111111111-1-1-1-1-1-11111-1-11-1111-1-11-1111111111111-1-1-1-1-1-11111-1-11-1111-1-11-1111111111111-1-1-1-1-1-11111-1-11-1111-1-11-1
χ4111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1111-11111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1111-11111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1111-11
χ5111-11111-1-11111-1-1-1-1-111111-1-1-1-1-1111-1111-11111-1-11111-1-1-1-1-111111-1-1-1-1-1111-1111-11111-1-11111-1-1-1-1-111111-1-1-1-1-1111-1
χ6111-11111-1-11111-1-1-1-1-111-1111-111-1-1-1-11111-11111-1-11111-1-1-1-1-111-1111-111-1-1-1-11111-11111-1-11111-1-1-1-1-111-1111-111-1-1-1-11
χ7111-11111-1-111-1-11111-1111-1-1-11-1-1-1-1-111111-11111-1-111-1-11111-1111-1-1-11-1-1-1-1-111111-11111-1-111-1-11111-1111-1-1-11-1-1-1-1-111
χ8111-11111-1-111-1-11111-111-1-1-11111-111-1-1111-11111-1-111-1-11111-111-1-1-11111-111-1-1111-11111-1-111-1-11111-111-1-1-11111-111-1-1
χ92222222222220000002-2-20000000-200002222222222220000002-2-20000000-200002222222222220000002-2-20000000-20000
χ10222-22222-2-222000000-2-2-2000000020000222-22222-2-222000000-2-2-2000000020000222-22222-2-222000000-2-2-2000000020000
χ1122-20222200-2-2002-2220-220000-2000000022-20222200-2-2002-2220-220000-2000000022-20222200-2-2002-2220-220000-20000000
χ1222-20222200-2-200-22-2-20-2200002000000022-20222200-2-200-22-2-20-2200002000000022-20222200-2-200-22-2-20-22000020000000
χ1322-20222200-2-22-2000002-202-200000000022-20222200-2-22-2000002-202-200000000022-20222200-2-22-2000002-202-2000000000
χ1422-20222200-2-2-22000002-20-2200000000022-20222200-2-2-22000002-20-2200000000022-20222200-2-2-22000002-20-22000000000
χ1544441-2-21-2-2-2100000010020020-1-1000-1044441-2-21-2-2-2100000010020020-1-1000-1044441-2-21-2-2-2100000010020020-1-1000-10
χ1644441-2-21-2-2-21000000100-200-20110001044441-2-21-2-2-21000000100-200-20110001044441-2-21-2-2-21000000100-200-201100010
χ174444-211-2111-22222-1-1-2000-1-10-100000004444-211-2111-22222-1-1-2000-1-10-100000004444-211-2111-22222-1-1-2000-1-10-10000000
χ184444-211-2111-2-2-2-2-211-2000110100000004444-211-2111-2-2-2-2-211-2000110100000004444-211-2111-2-2-2-2-211-200011010000000
χ19444-41-2-2122-21000000-100200-2011000-10444-41-2-2122-21000000-100200-2011000-10444-41-2-2122-21000000-100200-2011000-10
χ20444-41-2-2122-21000000-100-20020-1-100010444-41-2-2122-21000000-100-20020-1-100010444-41-2-2122-21000000-100-20020-1-100010
χ21444-4-211-2-1-11-222-2-2112000-1-1010000000444-4-211-2-1-11-222-2-2112000-1-1010000000444-4-211-2-1-11-222-2-2112000-1-1010000000
χ22444-4-211-2-1-11-2-2-222-1-12000110-10000000444-4-211-2-1-11-2-2-222-1-12000110-10000000444-4-211-2-1-11-2-2-222-1-12000110-10000000
χ2344-40-211-23-3-122-22-2-1-10000-1101000000044-40-211-23-3-122-22-2-1-10000-1101000000044-40-211-23-3-122-22-2-1-10000-11010000000
χ2444-40-211-23-3-12-22-221100001-10-1000000044-40-211-23-3-12-22-221100001-10-1000000044-40-211-23-3-12-22-221100001-10-10000000
χ2544-40-211-2-33-122-2-22110000-110-1000000044-40-211-2-33-122-2-22110000-110-1000000044-40-211-2-33-122-2-22110000-110-10000000
χ2644-40-211-2-33-12-222-2-1-100001-101000000044-40-211-2-33-12-222-2-1-100001-101000000044-40-211-2-33-12-222-2-1-100001-1010000000
χ274-40044-4-40000000000000000000002i−2i004-40044-4-40000000000000000000002i−2i004-40044-4-40000000000000000000002i−2i00
χ284-40044-4-4000000000000000000000−2i2i004-40044-4-4000000000000000000000−2i2i004-40044-4-4000000000000000000000−2i2i00
χ2988-802-4-42004-200000000000000000000088-802-4-42004-200000000000000000000088-802-4-42004-2000000000000000000000
χ308-8002-44-20000000000000000006−6000008-8002-44-20000000000000000006−6000008-8002-44-20000000000000000006−600000
χ318-8002-44-2000000000000000000−66000008-8002-44-2000000000000000000−66000008-8002-44-2000000000000000000−6600000
χ328-800-42-2400000000−2i32i30000000000000008-800-42-2400000000−2i32i30000000000000008-800-42-2400000000−2i32i3000000000000000
χ338-800-42-24000000002i3−2i30000000000000008-800-42-24000000002i3−2i30000000000000008-800-42-24000000002i3−2i3000000000000000
χ34111111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ35111111111111111111111-111-11-1-11-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32
χ36111111111111-1-1-1-1-1-11111-1-11-1111-1-11-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32
χ37111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1111-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32
χ38111-11111-1-11111-1-1-1-1-111111-1-1-1-1-1111-1−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i32
χ39111-11111-1-11111-1-1-1-1-111-1111-111-1-1-1-11−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32
χ40111-11111-1-111-1-11111-1111-1-1-11-1-1-1-1-111−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ41111-11111-1-111-1-11111-111-1-1-11111-111-1-1−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32
χ422222222222220000002-2-20000000-20000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3000000−1+i31−i31−i300000001−i30000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3000000−1−i31+i31+i300000001+i30000
χ43222-22222-2-222000000-2-2-2000000020000−1+i3−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i30000001−i31−i31−i30000000−1+i30000−1−i3−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i30000001+i31+i31+i30000000−1−i30000
χ4422-20222200-2-2002-2220-220000-20000000−1+i3−1+i31−i30−1+i3−1+i3−1+i3−1+i3001−i31−i300−1+i31−i3−1+i3−1+i301−i3−1+i300001−i30000000−1−i3−1−i31+i30−1−i3−1−i3−1−i3−1−i3001+i31+i300−1−i31+i3−1−i3−1−i301+i3−1−i300001+i30000000
χ4522-20222200-2-200-22-2-20-22000020000000−1+i3−1+i31−i30−1+i3−1+i3−1+i3−1+i3001−i31−i3001−i3−1+i31−i31−i301−i3−1+i30000−1+i30000000−1−i3−1−i31+i30−1−i3−1−i3−1−i3−1−i3001+i31+i3001+i3−1−i31+i31+i301+i3−1−i30000−1−i30000000
χ4622-20222200-2-22-2000002-202-2000000000−1+i3−1+i31−i30−1+i3−1+i3−1+i3−1+i3001−i31−i3−1+i31−i300000−1+i31−i30−1+i31−i3000000000−1−i3−1−i31+i30−1−i3−1−i3−1−i3−1−i3001+i31+i3−1−i31+i300000−1−i31+i30−1−i31+i3000000000
χ4722-20222200-2-2-22000002-20-22000000000−1+i3−1+i31−i30−1+i3−1+i3−1+i3−1+i3001−i31−i31−i3−1+i300000−1+i31−i301−i3−1+i3000000000−1−i3−1−i31+i30−1−i3−1−i3−1−i3−1−i3001+i31+i31+i3−1−i300000−1−i31+i301+i3−1−i3000000000
χ4844441-2-21-2-2-2100000010020020-1-1000-10−2+2i3−2+2i3−2+2i3−2+2i3−1+i321−i31−i3−1+i321−i31−i31−i3−1+i32000000−1+i3200−1+i300−1+i301−i321−i320001−i320−2−2i3−2−2i3−2−2i3−2−2i3−1−i321+i31+i3−1−i321+i31+i31+i3−1−i32000000−1−i3200−1−i300−1−i301+i321+i320001+i320
χ4944441-2-21-2-2-21000000100-200-201100010−2+2i3−2+2i3−2+2i3−2+2i3−1+i321−i31−i3−1+i321−i31−i31−i3−1+i32000000−1+i32001−i3001−i30−1+i32−1+i32000−1+i320−2−2i3−2−2i3−2−2i3−2−2i3−1−i321+i31+i3−1−i321+i31+i31+i3−1−i32000000−1−i32001+i3001+i30−1−i32−1−i32000−1−i320
χ504444-211-2111-22222-1-1-2000-1-10-10000000−2+2i3−2+2i3−2+2i3−2+2i31−i3−1+i32−1+i321−i3−1+i32−1+i32−1+i321−i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i30001−i321−i3201−i320000000−2−2i3−2−2i3−2−2i3−2−2i31+i3−1−i32−1−i321+i3−1−i32−1−i32−1−i321+i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i30001+i321+i3201+i320000000
χ514444-211-2111-2-2-2-2-211-200011010000000−2+2i3−2+2i3−2+2i3−2+2i31−i3−1+i32−1+i321−i3−1+i32−1+i32−1+i321−i31−i31−i31−i31−i3−1+i32−1+i321−i3000−1+i32−1+i320−1+i320000000−2−2i3−2−2i3−2−2i3−2−2i31+i3−1−i32−1−i321+i3−1−i32−1−i32−1−i321+i31+i31+i31+i31+i3−1−i32−1−i321+i3000−1−i32−1−i320−1−i320000000
χ52444-41-2-2122-21000000-100200-2011000-10−2+2i3−2+2i3−2+2i32−2i3−1+i321−i31−i3−1+i32−1+i3−1+i31−i3−1+i320000001−i3200−1+i3001−i30−1+i32−1+i320001−i320−2−2i3−2−2i3−2−2i32+2i3−1−i321+i31+i3−1−i32−1−i3−1−i31+i3−1−i320000001+i3200−1−i3001+i30−1−i32−1−i320001+i320
χ53444-41-2-2122-21000000-100-20020-1-100010−2+2i3−2+2i3−2+2i32−2i3−1+i321−i31−i3−1+i32−1+i3−1+i31−i3−1+i320000001−i32001−i300−1+i301−i321−i32000−1+i320−2−2i3−2−2i3−2−2i32+2i3−1−i321+i31+i3−1−i32−1−i3−1−i31+i3−1−i320000001+i32001+i300−1−i301+i321+i32000−1−i320
χ54444-4-211-2-1-11-222-2-2112000-1-1010000000−2+2i3−2+2i3−2+2i32−2i31−i3−1+i32−1+i321−i31−i321−i32−1+i321−i3−1+i3−1+i31−i31−i3−1+i32−1+i32−1+i30001−i321−i320−1+i320000000−2−2i3−2−2i3−2−2i32+2i31+i3−1−i32−1−i321+i31+i321+i32−1−i321+i3−1−i3−1−i31+i31+i3−1−i32−1−i32−1−i30001+i321+i320−1−i320000000
χ55444-4-211-2-1-11-2-2-222-1-12000110-10000000−2+2i3−2+2i3−2+2i32−2i31−i3−1+i32−1+i321−i31−i321−i32−1+i321−i31−i31−i3−1+i3−1+i31−i321−i32−1+i3000−1+i32−1+i3201−i320000000−2−2i3−2−2i3−2−2i32+2i31+i3−1−i32−1−i321+i31+i321+i32−1−i321+i31+i31+i3−1−i3−1−i31+i321+i32−1−i3000−1−i32−1−i3201+i320000000
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χ5744-40-211-23-3-12-22-221100001-10-10000000−2+2i3−2+2i32−2i301−i3−1+i32−1+i321−i3−3+3i323−3i321−i32−1+i31−i3−1+i31−i3−1+i3−1+i32−1+i320000−1+i321−i3201−i320000000−2−2i3−2−2i32+2i301+i3−1−i32−1−i321+i3−3−3i323+3i321+i32−1−i31+i3−1−i31+i3−1−i3−1−i32−1−i320000−1−i321+i3201+i320000000
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χ968-8002-44-20000000000000000006−600000−4−4i34+4i300−1−i32+2i3−2−2i31+i3000000000000000000−2ζ5−ζ7−ζ13−2ζ232ζ5+ζ7+ζ13+2ζ2300000−4+4i34−4i300−1+i32−2i3−2+2i31−i3000000000000000000ζ5+2ζ7+2ζ13+ζ23−ζ5−2ζ7−2ζ13−ζ2300000
χ978-8002-44-2000000000000000000−6600000−4−4i34+4i300−1−i32+2i3−2−2i31+i30000000000000000002ζ5+ζ7+ζ13+2ζ23−2ζ5−ζ7−ζ13−2ζ2300000−4+4i34−4i300−1+i32−2i3−2+2i31−i3000000000000000000−ζ5−2ζ7−2ζ13−ζ23ζ5+2ζ7+2ζ13+ζ2300000
χ988-800-42-2400000000−2i32i3000000000000000−4−4i34+4i3002+2i3−1−i31+i3−2−2i300000000−3+i33−i3000000000000000−4+4i34−4i3002−2i3−1+i31−i3−2+2i3000000003+i3−3−i3000000000000000
χ998-800-42-24000000002i3−2i3000000000000000−4−4i34+4i3002+2i3−1−i31+i3−2−2i3000000003−i3−3+i3000000000000000−4+4i34−4i3002−2i3−1+i31−i3−2+2i300000000−3−i33+i3000000000000000

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