Finite Group Databasebeta

← Group #13180876

Character table — Group #13180876

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size112222334466668899121216161616161616161818181818181818272736363636363636367272112222334466668899121216161616161616161818181818181818272736363636363636367272
order1233662236666636226633336666444444442212121212121212126622666622666666662266666666664444444422121212121212121266
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ31111111111111111-1-1111111111111-1-111-1-1-1-111-1-111-1-1-1-11111111111111111-1-1111111111111-1-111-1-1-1-111-1-111-1-1-1-1
χ41111111111111111-1-11111111111-1-111-1-111-1-1-1-111-1-111-1-11111111111111111-1-11111111111-1-111-1-111-1-1-1-111-1-111-1-1
χ51-111-1-11-11-111-1-11-11-11-11111-1-1-1-1i−ii−ii−ii−i1-1i−ii−ii−ii−i1-11-111-1-11-11-111-1-11-11-11-11111-1-1-1-1i−ii−ii−ii−i1-1i−ii−ii−ii−i1-1
χ61-111-1-11-11-111-1-11-11-11-11111-1-1-1-1−ii−ii−ii−ii1-1−ii−ii−ii−ii1-11-111-1-11-11-111-1-11-11-11-11111-1-1-1-1−ii−ii−ii−ii1-1−ii−ii−ii−ii1-1
χ71-111-1-11-11-111-1-11-1-111-11111-1-1-1-1i−i−iii−i−ii-11i−i−iii−i−ii-111-111-1-11-11-111-1-11-1-111-11111-1-1-1-1i−i−iii−i−ii-11i−i−iii−i−ii-11
χ81-111-1-11-11-111-1-11-1-111-11111-1-1-1-1−iii−i−iii−i-11−iii−i−iii−i-111-111-1-11-11-111-1-11-1-111-11111-1-1-1-1−iii−i−iii−i-11−iii−i−iii−i-11
χ922222222222222-1-12222-1-1-1-1-1-1-1-1000000002200000000-1-122222222222222-1-12222-1-1-1-1-1-1-1-1000000002200000000-1-1
χ1022222222222222-1-1-2-222-1-1-1-1-1-1-1-100000000-2-2000000001122222222222222-1-1-2-222-1-1-1-1-1-1-1-100000000-2-20000000011
χ11222-12-122-1-12-12-12200-1-12-1-1-12-1-1-1002200220000-1-100-1-100222-12-122-1-12-12-12200-1-12-1-1-12-1-1-1002200220000-1-100-1-100
χ12222-12-122-1-12-12-12200-1-12-1-1-12-1-1-100-2-200-2-2000011001100222-12-122-1-12-12-12200-1-12-1-1-12-1-1-100-2-200-2-2000011001100
χ1322-12-1222-1-1-12-122200-1-1-12-1-1-12-1-12200220000-1-100-1-1000022-12-1222-1-1-12-122200-1-1-12-1-1-12-1-12200220000-1-100-1-10000
χ1422-12-1222-1-1-12-122200-1-1-12-1-1-12-1-1-2-200-2-20000110011000022-12-1222-1-1-12-122200-1-1-12-1-1-12-1-1-2-200-2-200001100110000
χ152-222-2-22-22-222-2-2-112-22-2-1-1-1-11111000000002-200000000-112-222-2-22-22-222-2-2-112-22-2-1-1-1-11111000000002-200000000-11
χ162-222-2-22-22-222-2-2-11-222-2-1-1-1-1111100000000-22000000001-12-222-2-22-22-222-2-2-11-222-2-1-1-1-1111100000000-22000000001-1
χ172-22-1-212-2-112-1-212-200-112-1-1-1-2111002i−2i002i−2i0000−ii00−ii002-22-1-212-2-112-1-212-200-112-1-1-1-2111002i−2i002i−2i0000−ii00−ii00
χ182-22-1-212-2-112-1-212-200-112-1-1-1-211100−2i2i00−2i2i0000i−i00i−i002-22-1-212-2-112-1-212-200-112-1-1-1-211100−2i2i00−2i2i0000i−i00i−i00
χ192-2-121-22-2-11-121-22-200-11-12-1-11-2112i−2i002i−2i0000−ii00−ii00002-2-121-22-2-11-121-22-200-11-12-1-11-2112i−2i002i−2i0000−ii00−ii0000
χ202-2-121-22-2-11-121-22-200-11-12-1-11-211−2i2i00−2i2i0000i−i00i−i00002-2-121-22-2-11-121-22-200-11-12-1-11-211−2i2i00−2i2i0000i−i00i−i0000
χ21333333-1-133-1-1-1-10033-1-1000000001111-1-1-1-1-1-11111-1-1-1-100333333-1-133-1-1-1-10033-1-1000000001111-1-1-1-1-1-11111-1-1-1-100
χ22333333-1-133-1-1-1-10033-1-100000000-1-1-1-11111-1-1-1-1-1-1111100333333-1-133-1-1-1-10033-1-100000000-1-1-1-11111-1-1-1-1-1-1111100
χ23333333-1-133-1-1-1-100-3-3-1-10000000011-1-1-1-1111111-1-1-1-11100333333-1-133-1-1-1-100-3-3-1-10000000011-1-1-1-1111111-1-1-1-11100
χ24333333-1-133-1-1-1-100-3-3-1-100000000-1-11111-1-111-1-11111-1-100333333-1-133-1-1-1-100-3-3-1-100000000-1-11111-1-111-1-11111-1-100
χ253-333-3-3-113-3-1-111003-3-1100000000i−ii−i−ii−ii-11i−ii−i−ii−ii003-333-3-3-113-3-1-111003-3-1100000000i−ii−i−ii−ii-11i−ii−i−ii−ii00
χ263-333-3-3-113-3-1-111003-3-1100000000−ii−iii−ii−i-11−ii−iii−ii−i003-333-3-3-113-3-1-111003-3-1100000000−ii−iii−ii−i-11−ii−iii−ii−i00
χ273-333-3-3-113-3-1-11100-33-1100000000i−i−ii−iii−i1-1i−i−ii−iii−i003-333-3-3-113-3-1-11100-33-1100000000i−i−ii−iii−i1-1i−i−ii−iii−i00
χ283-333-3-3-113-3-1-11100-33-1100000000−iii−ii−i−ii1-1−iii−ii−i−ii003-333-3-3-113-3-1-11100-33-1100000000−iii−ii−i−ii1-1−iii−ii−i−ii00
χ29444-24-244-2-24-24-2-2-200-2-2-2111-211100000000000000000000444-24-244-2-24-24-2-2-200-2-2-2111-211100000000000000000000
χ3044-24-2444-2-2-24-24-2-200-2-21-2111-2110000000000000000000044-24-2444-2-2-24-24-2-200-2-21-2111-21100000000000000000000
χ3144-2-2-2-24411-2-2-2-2440011-2-211-2-2110000000000000000000044-2-2-2-24411-2-2-2-2440011-2-211-2-21100000000000000000000
χ3244-2-2-2-24411-2-2-2-2-2-2001111−1−3i32−1+3i3211−1−3i32−1+3i320000000000000000000044-2-2-2-24411-2-2-2-2-2-2001111−1−3i32−1+3i3211−1−3i32−1+3i3200000000000000000000
χ3344-2-2-2-24411-2-2-2-2-2-2001111−1+3i32−1−3i3211−1+3i32−1−3i320000000000000000000044-2-2-2-24411-2-2-2-2-2-2001111−1+3i32−1−3i3211−1+3i32−1−3i3200000000000000000000
χ344-44-2-424-4-224-2-42-2200-22-21112-1-1-1000000000000000000004-44-2-424-4-224-2-42-2200-22-21112-1-1-100000000000000000000
χ354-4-242-44-4-22-242-4-2200-221-211-12-1-1000000000000000000004-4-242-44-4-22-242-4-2200-221-211-12-1-100000000000000000000
χ364-4-2-2224-41-1-2-2224-4001-1-2-21122-1-1000000000000000000004-4-2-2224-41-1-2-2224-4001-1-2-21122-1-100000000000000000000
χ374-4-2-2224-41-1-2-222-22001-111−1−3i32−1+3i32-1-11+3i321−3i32000000000000000000004-4-2-2224-41-1-2-222-22001-111−1−3i32−1+3i32-1-11+3i321−3i3200000000000000000000
χ384-4-2-2224-41-1-2-222-22001-111−1+3i32−1−3i32-1-11−3i321+3i32000000000000000000004-4-2-2224-41-1-2-222-22001-111−1+3i32−1−3i32-1-11−3i321+3i3200000000000000000000
χ39666-36-3-2-2-3-3-21-2100001100000000002200-2-20000-1-1001100666-36-3-2-2-3-3-21-2100001100000000002200-2-20000-1-1001100
χ40666-36-3-2-2-3-3-21-210000110000000000-2-2002200001100-1-100666-36-3-2-2-3-3-21-210000110000000000-2-2002200001100-1-100
χ4166-36-36-2-2-3-31-21-2000011000000002200-2-20000-1-10011000066-36-36-2-2-3-31-21-2000011000000002200-2-20000-1-100110000
χ4266-36-36-2-2-3-31-21-200001100000000-2-2002200001100-1-1000066-36-36-2-2-3-31-21-200001100000000-2-2002200001100-1-10000
χ436-66-3-63-22-33-212-100001-100000000002i−2i00−2i2i0000−ii00i−i006-66-3-63-22-33-212-100001-100000000002i−2i00−2i2i0000−ii00i−i00
χ446-66-3-63-22-33-212-100001-10000000000−2i2i002i−2i0000i−i00−ii006-66-3-63-22-33-212-100001-10000000000−2i2i002i−2i0000i−i00−ii00
χ456-6-363-6-22-331-2-1200001-1000000002i−2i00−2i2i0000−ii00i−i00006-6-363-6-22-331-2-1200001-1000000002i−2i00−2i2i0000−ii00i−i0000
χ466-6-363-6-22-331-2-1200001-100000000−2i2i002i−2i0000i−i00−ii00006-6-363-6-22-331-2-1200001-100000000−2i2i002i−2i0000i−i00−ii0000
χ471212-6-6-6-6-4-43322220000-1-100000000000000000000000000001212-6-6-6-6-4-43322220000-1-10000000000000000000000000000
χ4812-12-6-666-443-322-2-20000-11000000000000000000000000000012-12-6-666-443-322-2-20000-110000000000000000000000000000
χ49111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ501111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1
χ511111111111111111-1-1111111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111
χ521111111111111111-1-11111111111-1-111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-111
χ531-111-1-11-11-111-1-11-11-11-11111-1-1-1-1i−ii−ii−ii−i1-1i−ii−ii−ii−i1-1-11-1-111-11-11-1-111-11-11-11-1-1-1-11111−ii−ii−ii−ii-11−ii−ii−ii−ii-11
χ541-111-1-11-11-111-1-11-11-11-11111-1-1-1-1−ii−ii−ii−ii1-1−ii−ii−ii−ii1-1-11-1-111-11-11-1-111-11-11-11-1-1-1-11111i−ii−ii−ii−i-11i−ii−ii−ii−i-11
χ551-111-1-11-11-111-1-11-1-111-11111-1-1-1-1i−i−iii−i−ii-11i−i−iii−i−ii-11-11-1-111-11-11-1-111-111-1-11-1-1-1-11111−iii−i−iii−i1-1−iii−i−iii−i1-1
χ561-111-1-11-11-111-1-11-1-111-11111-1-1-1-1−iii−i−iii−i-11−iii−i−iii−i-11-11-1-111-11-11-1-111-111-1-11-1-1-1-11111i−i−iii−i−ii1-1i−i−iii−i−ii1-1
χ5722222222222222-1-12222-1-1-1-1-1-1-1-1000000002200000000-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-211-2-2-2-21111111100000000-2-20000000011
χ5822222222222222-1-1-2-222-1-1-1-1-1-1-1-100000000-2-20000000011-2-2-2-2-2-2-2-2-2-2-2-2-2-21122-2-211111111000000002200000000-1-1
χ59222-12-122-1-12-12-12200-1-12-1-1-12-1-1-1002200220000-1-100-1-100-2-2-21-21-2-211-21-21-2-20011-2111-211100-2-200-2-2000011001100
χ60222-12-122-1-12-12-12200-1-12-1-1-12-1-1-100-2-200-2-2000011001100-2-2-21-21-2-211-21-21-2-20011-2111-2111002200220000-1-100-1-100
χ6122-12-1222-1-1-12-122200-1-1-12-1-1-12-1-12200220000-1-100-1-10000-2-21-21-2-2-2111-21-2-2-200111-2111-211-2-200-2-200001100110000
χ6222-12-1222-1-1-12-122200-1-1-12-1-1-12-1-1-2-200-2-200001100110000-2-21-21-2-2-2111-21-2-2-200111-2111-2112200220000-1-100-1-10000
χ632-222-2-22-22-222-2-2-112-22-2-1-1-1-11111000000002-200000000-11-22-2-222-22-22-2-2221-1-22-221111-1-1-1-100000000-22000000001-1
χ642-222-2-22-22-222-2-2-11-222-2-1-1-1-1111100000000-22000000001-1-22-2-222-22-22-2-2221-12-2-221111-1-1-1-1000000002-200000000-11
χ652-22-1-212-2-112-1-212-200-112-1-1-1-2111002i−2i002i−2i0000−ii00−ii00-22-212-1-221-1-212-1-22001-1-21112-1-1-100−2i2i00−2i2i0000i−i00i−i00
χ662-22-1-212-2-112-1-212-200-112-1-1-1-211100−2i2i00−2i2i0000i−i00i−i00-22-212-1-221-1-212-1-22001-1-21112-1-1-1002i−2i002i−2i0000−ii00−ii00
χ672-2-121-22-2-11-121-22-200-11-12-1-11-2112i−2i002i−2i0000−ii00−ii0000-221-2-12-221-11-2-12-22001-11-211-12-1-1−2i2i00−2i2i0000i−i00i−i0000
χ682-2-121-22-2-11-121-22-200-11-12-1-11-211−2i2i00−2i2i0000i−i00i−i0000-221-2-12-221-11-2-12-22001-11-211-12-1-12i−2i002i−2i0000−ii00−ii0000
χ69333333-1-133-1-1-1-10033-1-1000000001111-1-1-1-1-1-11111-1-1-1-100-3-3-3-3-3-311-3-3111100-3-31100000000-1-1-1-1111111-1-1-1-1111100
χ70333333-1-133-1-1-1-10033-1-100000000-1-1-1-11111-1-1-1-1-1-1111100-3-3-3-3-3-311-3-3111100-3-311000000001111-1-1-1-1111111-1-1-1-100
χ71333333-1-133-1-1-1-100-3-3-1-10000000011-1-1-1-1111111-1-1-1-11100-3-3-3-3-3-311-3-3111100331100000000-1-11111-1-1-1-1-1-11111-1-100
χ72333333-1-133-1-1-1-100-3-3-1-100000000-1-11111-1-111-1-11111-1-100-3-3-3-3-3-311-3-311110033110000000011-1-1-1-111-1-111-1-1-1-11100
χ733-333-3-3-113-3-1-111003-3-1100000000i−ii−i−ii−ii-11i−ii−i−ii−ii00-33-3-3331-1-3311-1-100-331-100000000−ii−iii−ii−i1-1−ii−iii−ii−i00
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χ753-333-3-3-113-3-1-11100-33-1100000000i−i−ii−iii−i1-1i−i−ii−iii−i00-33-3-3331-1-3311-1-1003-31-100000000−iii−ii−i−ii-11−iii−ii−i−ii00
χ763-333-3-3-113-3-1-11100-33-1100000000−iii−ii−i−ii1-1−iii−ii−i−ii00-33-3-3331-1-3311-1-1003-31-100000000i−i−ii−iii−i-11i−i−ii−iii−i00
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χ7844-24-2444-2-2-24-24-2-200-2-21-2111-21100000000000000000000-4-42-42-4-4-4222-42-4220022-12-1-1-12-1-100000000000000000000
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χ8144-2-2-2-24411-2-2-2-2-2-2001111−1+3i32−1−3i3211−1+3i32−1−3i3200000000000000000000-4-42222-4-4-1-122222200-1-1-1-11−3i321+3i32-1-11−3i321+3i3200000000000000000000
χ824-44-2-424-4-224-2-42-2200-22-21112-1-1-100000000000000000000-44-424-2-442-2-424-22-2002-22-1-1-1-211100000000000000000000
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χ844-4-2-2224-41-1-2-2224-4001-1-2-21122-1-100000000000000000000-4422-2-2-44-1122-2-2-4400-1122-1-1-2-21100000000000000000000
χ854-4-2-2224-41-1-2-222-22001-111−1−3i32−1+3i32-1-11+3i321−3i3200000000000000000000-4422-2-2-44-1122-2-22-200-11-1-11+3i321−3i3211−1−3i32−1+3i3200000000000000000000
χ864-4-2-2224-41-1-2-222-22001-111−1+3i32−1−3i32-1-11−3i321+3i3200000000000000000000-4422-2-2-44-1122-2-22-200-11-1-11−3i321+3i3211−1+3i32−1−3i3200000000000000000000
χ87666-36-3-2-2-3-3-21-2100001100000000002200-2-20000-1-1001100-6-6-63-6322332-12-10000-1-10000000000-2-2002200001100-1-100
χ88666-36-3-2-2-3-3-21-210000110000000000-2-2002200001100-1-100-6-6-63-6322332-12-10000-1-100000000002200-2-20000-1-1001100
χ8966-36-36-2-2-3-31-21-2000011000000002200-2-20000-1-100110000-6-63-63-62233-12-120000-1-100000000-2-2002200001100-1-10000
χ9066-36-36-2-2-3-31-21-200001100000000-2-2002200001100-1-10000-6-63-63-62233-12-120000-1-1000000002200-2-20000-1-100110000
χ916-66-3-63-22-33-212-100001-100000000002i−2i00−2i2i0000−ii00i−i00-66-636-32-23-32-1-210000-110000000000−2i2i002i−2i0000i−i00−ii00
χ926-66-3-63-22-33-212-100001-10000000000−2i2i002i−2i0000i−i00−ii00-66-636-32-23-32-1-210000-1100000000002i−2i00−2i2i0000−ii00i−i00
χ936-6-363-6-22-331-2-1200001-1000000002i−2i00−2i2i0000−ii00i−i0000-663-6-362-23-3-121-20000-1100000000−2i2i002i−2i0000i−i00−ii0000
χ946-6-363-6-22-331-2-1200001-100000000−2i2i002i−2i0000i−i00−ii0000-663-6-362-23-3-121-20000-11000000002i−2i00−2i2i0000−ii00i−i0000
χ951212-6-6-6-6-4-43322220000-1-10000000000000000000000000000-12-12666644-3-3-2-2-2-20000110000000000000000000000000000
χ9612-12-6-666-443-322-2-20000-110000000000000000000000000000-121266-6-64-4-33-2-22200001-10000000000000000000000000000

Here i is the imaginary unit (i² = −1).