Finite Group Databasebeta

← Group #13180872

Character table — Group #13180872

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size112222334466668899121216161616161616161818181818181818272736363636363636367272112222334466668899121216161616161616161818181818181818272736363636363636367272
order1233662236666636446633336666224444444466121212121212121222666622666666664466666666662244444444661212121212121212
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
χ51-111-1-11-11-11-1-111-1i−i1-11111-1-1-1-11-1i−i1-1i−ii−i1-1i−i1-1i−ii−i1-111-1-11-11-11-1-111-1i−i1-11111-1-1-1-11-1i−i1-1i−ii−i1-1i−i1-1i−ii−i
χ61-111-1-11-11-11-1-111-1i−i1-11111-1-1-1-1-11−ii-11−iii−i-11−ii-11−iii−i1-111-1-11-11-11-1-111-1i−i1-11111-1-1-1-1-11−ii-11−iii−i-11−ii-11−iii−i
χ71-111-1-11-11-11-1-111-1−ii1-11111-1-1-1-11-1−ii1-1−ii−ii1-1−ii1-1−ii−ii1-111-1-11-11-11-1-111-1−ii1-11111-1-1-1-11-1−ii1-1−ii−ii1-1−ii1-1−ii−ii
χ81-111-1-11-11-11-1-111-1−ii1-11111-1-1-1-1-11i−i-11i−i−ii-11i−i-11i−i−ii1-111-1-11-11-11-1-111-1−ii1-11111-1-1-1-1-11i−i-11i−i−ii-11i−i-11i−i−ii
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
χ11222-1-1222-1-12-12-12200-1-12-1-1-12-1-1-12200220000-1-100-1-10000222-1-1222-1-12-12-12200-1-12-1-1-12-1-1-12200220000-1-100-1-10000
χ12222-1-1222-1-12-12-12200-1-12-1-1-12-1-1-1-2-200-2-200001100110000222-1-1222-1-12-12-12200-1-12-1-1-12-1-1-1-2-200-2-200001100110000
χ1322-122-122-1-1-12-122200-1-1-12-1-1-12-1-1002200220000-1-100-1-10022-122-122-1-1-12-122200-1-1-12-1-1-12-1-1002200220000-1-100-1-100
χ1422-122-122-1-1-12-122200-1-1-12-1-1-12-1-100-2-200-2-200001100110022-122-122-1-1-12-122200-1-1-12-1-1-12-1-100-2-200-2-2000011001100
χ152-222-2-22-22-22-2-22-112i−2i2-2-1-1-1-11111000000002i−2i00000000−ii2-222-2-22-22-22-2-22-112i−2i2-2-1-1-1-11111000000002i−2i00000000−ii
χ162-222-2-22-22-22-2-22-11−2i2i2-2-1-1-1-1111100000000−2i2i00000000i−i2-222-2-22-22-22-2-22-11−2i2i2-2-1-1-1-1111100000000−2i2i00000000i−i
χ172-22-11-22-2-1121-2-12-200-112-1-1-1-21112-2002-20000-1100-1100002-22-11-22-2-1121-2-12-200-112-1-1-1-21112-2002-20000-1100-110000
χ182-22-11-22-2-1121-2-12-200-112-1-1-1-2111-2200-2200001-1001-100002-22-11-22-2-1121-2-12-200-112-1-1-1-2111-2200-2200001-1001-10000
χ192-2-12-212-2-11-1-2122-200-11-12-1-11-211002i−2i002i−2i0000−ii00−ii002-2-12-212-2-11-1-2122-200-11-12-1-11-211002i−2i002i−2i0000−ii00−ii00
χ202-2-12-212-2-11-1-2122-200-11-12-1-11-21100−2i2i00−2i2i0000i−i00i−i002-2-12-212-2-11-1-2122-200-11-12-1-11-21100−2i2i00−2i2i0000i−i00i−i00
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
χ253-333-3-3-113-3-111-1003i−3i-11000000001-1i−i-11−ii−ii1-1i−i-11−ii003-333-3-3-113-3-111-1003i−3i-11000000001-1i−i-11−ii−ii1-1i−i-11−ii00
χ263-333-3-3-113-3-111-1003i−3i-1100000000-11−ii1-1i−i−ii-11−ii1-1i−i003-333-3-3-113-3-111-1003i−3i-1100000000-11−ii1-1i−i−ii-11−ii1-1i−i00
χ273-333-3-3-113-3-111-100−3i3i-11000000001-1−ii-11i−ii−i1-1−ii-11i−i003-333-3-3-113-3-111-100−3i3i-11000000001-1−ii-11i−ii−i1-1−ii-11i−i00
χ283-333-3-3-113-3-111-100−3i3i-1100000000-11i−i1-1−iii−i-11i−i1-1−ii003-333-3-3-113-3-111-100−3i3i-1100000000-11i−i1-1−iii−i-11i−i1-1−ii00
χ29444-2-2444-2-24-24-2-2-200-2-2-2111-211100000000000000000000444-2-2444-2-24-24-2-2-200-2-2-2111-211100000000000000000000
χ3044-244-244-2-2-24-24-2-200-2-21-2111-2110000000000000000000044-244-244-2-2-24-24-2-200-2-21-2111-21100000000000000000000
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
χ344-44-22-44-4-2242-4-2-2200-22-21112-1-1-1000000000000000000004-44-22-44-4-2242-4-2-2200-22-21112-1-1-100000000000000000000
χ354-4-24-424-4-22-2-424-2200-221-211-12-1-1000000000000000000004-4-24-424-4-22-2-424-2200-221-211-12-1-100000000000000000000
χ364-4-2-2224-41-1-222-24-4001-1-2-21122-1-1000000000000000000004-4-2-2224-41-1-222-24-4001-1-2-21122-1-100000000000000000000
χ374-4-2-2224-41-1-222-2-22001-111−1−3i32−1+3i32-1-11+3i321−3i32000000000000000000004-4-2-2224-41-1-222-2-22001-111−1−3i32−1+3i32-1-11+3i321−3i3200000000000000000000
χ384-4-2-2224-41-1-222-2-22001-111−1+3i32−1−3i32-1-11−3i321+3i32000000000000000000004-4-2-2224-41-1-222-2-22001-111−1+3i32−1−3i32-1-11−3i321+3i3200000000000000000000
χ39666-3-36-2-2-3-3-21-21000011000000002200-2-20000-1-100110000666-3-36-2-2-3-3-21-21000011000000002200-2-20000-1-100110000
χ40666-3-36-2-2-3-3-21-2100001100000000-2-2002200001100-1-10000666-3-36-2-2-3-3-21-2100001100000000-2-2002200001100-1-10000
χ4166-366-3-2-2-3-31-21-200001100000000002200-2-20000-1-100110066-366-3-2-2-3-31-21-200001100000000002200-2-20000-1-1001100
χ4266-366-3-2-2-3-31-21-20000110000000000-2-2002200001100-1-10066-366-3-2-2-3-31-21-20000110000000000-2-2002200001100-1-100
χ436-66-33-6-22-33-2-12100001-1000000002-200-220000-11001-100006-66-33-6-22-33-2-12100001-1000000002-200-220000-11001-10000
χ446-66-33-6-22-33-2-12100001-100000000-22002-200001-100-1100006-66-33-6-22-33-2-12100001-100000000-22002-200001-100-110000
χ456-6-36-63-22-3312-1-200001-100000000002i−2i00−2i2i0000−ii00i−i006-6-36-63-22-3312-1-200001-100000000002i−2i00−2i2i0000−ii00i−i00
χ466-6-36-63-22-3312-1-200001-10000000000−2i2i002i−2i0000i−i00−ii006-6-36-63-22-3312-1-200001-10000000000−2i2i002i−2i0000i−i00−ii00
χ471212-6-6-6-6-4-43322220000-1-100000000000000000000000000001212-6-6-6-6-4-43322220000-1-10000000000000000000000000000
χ4812-12-6-666-443-32-2-220000-11000000000000000000000000000012-12-6-666-443-32-2-220000-110000000000000000000000000000
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
χ531-111-1-11-11-11-1-111-1i−i1-11111-1-1-1-11-1i−i1-1i−ii−i1-1i−i1-1i−ii−i-11-1-111-11-11-111-1-11−ii-11-1-1-1-11111-11−ii-11−ii−ii-11−ii-11−ii−ii
χ541-111-1-11-11-11-1-111-1i−i1-11111-1-1-1-1-11−ii-11−iii−i-11−ii-11−iii−i-11-1-111-11-11-111-1-11−ii-11-1-1-1-111111-1i−i1-1i−i−ii1-1i−i1-1i−i−ii
χ551-111-1-11-11-11-1-111-1−ii1-11111-1-1-1-11-1−ii1-1−ii−ii1-1−ii1-1−ii−ii-11-1-111-11-11-111-1-11i−i-11-1-1-1-11111-11i−i-11i−ii−i-11i−i-11i−ii−i
χ561-111-1-11-11-11-1-111-1−ii1-11111-1-1-1-1-11i−i-11i−i−ii-11i−i-11i−i−ii-11-1-111-11-11-111-1-11i−i-11-1-1-1-111111-1−ii1-1−iii−i1-1−ii1-1−iii−i
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
χ59222-1-1222-1-12-12-12200-1-12-1-1-12-1-1-12200220000-1-100-1-10000-2-2-211-2-2-211-21-21-2-20011-2111-2111-2-200-2-200001100110000
χ60222-1-1222-1-12-12-12200-1-12-1-1-12-1-1-1-2-200-2-200001100110000-2-2-211-2-2-211-21-21-2-20011-2111-21112200220000-1-100-1-10000
χ6122-122-122-1-1-12-122200-1-1-12-1-1-12-1-1002200220000-1-100-1-100-2-21-2-21-2-2111-21-2-2-200111-2111-21100-2-200-2-2000011001100
χ6222-122-122-1-1-12-122200-1-1-12-1-1-12-1-100-2-200-2-2000011001100-2-21-2-21-2-2111-21-2-2-200111-2111-211002200220000-1-100-1-100
χ632-222-2-22-22-22-2-22-112i−2i2-2-1-1-1-11111000000002i−2i00000000−ii-22-2-222-22-22-222-21-1−2i2i-221111-1-1-1-100000000−2i2i00000000i−i
χ642-222-2-22-22-22-2-22-11−2i2i2-2-1-1-1-1111100000000−2i2i00000000i−i-22-2-222-22-22-222-21-12i−2i-221111-1-1-1-1000000002i−2i00000000−ii
χ652-22-11-22-2-1121-2-12-200-112-1-1-1-21112-2002-20000-1100-110000-22-21-12-221-1-2-121-22001-1-21112-1-1-1-2200-2200001-1001-10000
χ662-22-11-22-2-1121-2-12-200-112-1-1-1-2111-2200-2200001-1001-10000-22-21-12-221-1-2-121-22001-1-21112-1-1-12-2002-20000-1100-110000
χ672-2-12-212-2-11-1-2122-200-11-12-1-11-211002i−2i002i−2i0000−ii00−ii00-221-22-1-221-112-1-2-22001-11-211-12-1-100−2i2i00−2i2i0000i−i00i−i00
χ682-2-12-212-2-11-1-2122-200-11-12-1-11-21100−2i2i00−2i2i0000i−i00i−i00-221-22-1-221-112-1-2-22001-11-211-12-1-1002i−2i002i−2i0000−ii00−ii00
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
χ733-333-3-3-113-3-111-1003i−3i-11000000001-1i−i-11−ii−ii1-1i−i-11−ii00-33-3-3331-1-331-1-1100−3i3i1-100000000-11−ii1-1i−ii−i-11−ii1-1i−i00
χ743-333-3-3-113-3-111-1003i−3i-1100000000-11−ii1-1i−i−ii-11−ii1-1i−i00-33-3-3331-1-331-1-1100−3i3i1-1000000001-1i−i-11−iii−i1-1i−i-11−ii00
χ753-333-3-3-113-3-111-100−3i3i-11000000001-1−ii-11i−ii−i1-1−ii-11i−i00-33-3-3331-1-331-1-11003i−3i1-100000000-11i−i1-1−ii−ii-11i−i1-1−ii00
χ763-333-3-3-113-3-111-100−3i3i-1100000000-11i−i1-1−iii−i-11i−i1-1−ii00-33-3-3331-1-331-1-11003i−3i1-1000000001-1−ii-11i−i−ii1-1−ii-11i−i00
χ77444-2-2444-2-24-24-2-2-200-2-2-2111-211100000000000000000000-4-4-422-4-4-422-42-422200222-1-1-12-1-1-100000000000000000000
χ7844-244-244-2-2-24-24-2-200-2-21-2111-21100000000000000000000-4-42-4-42-4-4222-42-4220022-12-1-1-12-1-100000000000000000000
χ7944-2-2-2-24411-2-2-2-2440011-2-211-2-21100000000000000000000-4-42222-4-4-1-12222-4-400-1-122-1-122-1-100000000000000000000
χ8044-2-2-2-24411-2-2-2-2-2-2001111−1−3i32−1+3i3211−1−3i32−1+3i3200000000000000000000-4-42222-4-4-1-122222200-1-1-1-11+3i321−3i32-1-11+3i321−3i3200000000000000000000
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
χ824-44-22-44-4-2242-4-2-2200-22-21112-1-1-100000000000000000000-44-42-24-442-2-4-2422-2002-22-1-1-1-211100000000000000000000
χ834-4-24-424-4-22-2-424-2200-221-211-12-1-100000000000000000000-442-44-2-442-224-2-42-2002-2-12-1-11-21100000000000000000000
χ844-4-2-2224-41-1-222-24-4001-1-2-21122-1-100000000000000000000-4422-2-2-44-112-2-22-4400-1122-1-1-2-21100000000000000000000
χ854-4-2-2224-41-1-222-2-22001-111−1−3i32−1+3i32-1-11+3i321−3i3200000000000000000000-4422-2-2-44-112-2-222-200-11-1-11+3i321−3i3211−1−3i32−1+3i3200000000000000000000
χ864-4-2-2224-41-1-222-2-22001-111−1+3i32−1−3i32-1-11−3i321+3i3200000000000000000000-4422-2-2-44-112-2-222-200-11-1-11−3i321+3i3211−1+3i32−1−3i3200000000000000000000
χ87666-3-36-2-2-3-3-21-21000011000000002200-2-20000-1-100110000-6-6-633-622332-12-10000-1-100000000-2-2002200001100-1-10000
χ88666-3-36-2-2-3-3-21-2100001100000000-2-2002200001100-1-10000-6-6-633-622332-12-10000-1-1000000002200-2-20000-1-100110000
χ8966-366-3-2-2-3-31-21-200001100000000002200-2-20000-1-1001100-6-63-6-632233-12-120000-1-10000000000-2-2002200001100-1-100
χ9066-366-3-2-2-3-31-21-20000110000000000-2-2002200001100-1-100-6-63-6-632233-12-120000-1-100000000002200-2-20000-1-1001100
χ916-66-33-6-22-33-2-12100001-1000000002-200-220000-11001-10000-66-63-362-23-321-2-10000-1100000000-22002-200001-100-110000
χ926-66-33-6-22-33-2-12100001-100000000-22002-200001-100-110000-66-63-362-23-321-2-10000-11000000002-200-220000-11001-10000
χ936-6-36-63-22-3312-1-200001-100000000002i−2i00−2i2i0000−ii00i−i00-663-66-32-23-3-1-2120000-110000000000−2i2i002i−2i0000i−i00−ii00
χ946-6-36-63-22-3312-1-200001-10000000000−2i2i002i−2i0000i−i00−ii00-663-66-32-23-3-1-2120000-1100000000002i−2i00−2i2i0000−ii00i−i00
χ951212-6-6-6-6-4-43322220000-1-10000000000000000000000000000-12-12666644-3-3-2-2-2-20000110000000000000000000000000000
χ9612-12-6-666-443-32-2-220000-110000000000000000000000000000-121266-6-64-4-33-222-200001-10000000000000000000000000000

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