Finite Group Databasebeta

← Group #13180879

Character table — Group #13180879

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1122222334444446666688889912121212121216161616161616161616161616161616182727363636363636363654727272727272727272727272
order122336622366666266663666226666663333666666666666222224444442666666121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1
χ3111111111111111111111111-1-11111111111111111111111-1-1-11-11-111-1-1-11-1-1-1-1-11-111-1-1
χ4111111111111111111111111-1-11111111111111111111111-1-1-1-11-11-1-111-1-11-1-1-1-1-11-1-111
χ511-11111111-1-11-1-1-1111111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-11111-1-11-11-1-11111-1-1-1-11-11-1
χ611-11111111-1-11-1-1-1111111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-111-1-111-11-11-1-1-111-1-111-11-11
χ711-11111111-1-11-1-1-1111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11-1-11-1-111-1-1111-1-1-111-111-1-11
χ811-11111111-1-11-1-1-1111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11-1-1-111-1-111-11-11-1-1111-1-111-1
χ922222222222222222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122200000000200-1-1-1-1000000
χ1022222222222222222222-1-1-1-1-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-200000000-2001111000000
χ112222-12-122-12-1-1-1-1222-1-12222002-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-10000202002200-100000-100-1-1
χ122222-12-122-12-1-1-1-1222-1-12222002-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-10000-20-200-2-20010000010011
χ13222-12-1222-1-12-1-1-12-1-122222200-12-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1000202022000-100000-10-1-100
χ14222-12-1222-1-12-1-1-12-1-122222200-12-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1000-20-20-2-2000100000101100
χ1522-22222222-2-22-2-2-22222-1-11122-2-222-2-2-1-1-1-1-1-1-1-111111111-22200000000-200-1-111000000
χ1622-22222222-2-22-2-2-22222-1-111-2-2-2-222-2-2-1-1-1-1-1-1-1-1111111112-2-20000000020011-1-1000000
χ1722-22-12-122-1-21-111-222-1-122-2-200-21-1-1112-1-1-12-1-1-1-2-2111111000020-2002-200-100000100-11
χ1822-22-12-122-1-21-111-222-1-122-2-200-21-1-1112-1-1-12-1-1-1-2-21111110000-20200-2200100000-1001-1
χ1922-2-12-1222-11-2-111-2-1-12222-2-2001-2-1-111-12-1-1-12-1-111-2-2111100020-202-2000-10000010-1100
χ2022-2-12-1222-11-2-111-2-1-12222-2-2001-2-1-111-12-1-1-12-1-111-2-21111000-2020-22000100000-101-100
χ212-2022-2-22-2200-20002-22-22-2002-2002-2002222-2-2-2-20000000002-2000000000002-200000000
χ222-2022-2-22-2200-20002-22-22-200-22002-2002222-2-2-2-2000000000-2200000000000-2200000000
χ232-2022-2-22-2200-20002-22-2-11i3−i32-2002-200-1-1-1-11111i3−i3i3−i3i3i3−i3−i302-200000000000-11i3−i3000000
χ242-2022-2-22-2200-20002-22-2-11i3−i3-22002-200-1-1-1-11111i3−i3i3−i3i3i3−i3−i30-22000000000001-1−i3i3000000
χ252-2022-2-22-2200-20002-22-2-11−i3i32-2002-200-1-1-1-11111−i3i3−i3i3−i3−i3i3i302-200000000000-11−i3i3000000
χ262-2022-2-22-2200-20002-22-2-11−i3i3-22002-200-1-1-1-11111−i3i3−i3i3−i3−i3i3i30-22000000000001-1i3−i3000000
χ273333333-1-1333333-1-1-1-1-1000033-1-1-1-1-1-100000000000000003-1-11111-1-1-1-1-111000011-1-1-1-1
χ283333333-1-1333333-1-1-1-1-1000033-1-1-1-1-1-100000000000000003-1-1-1-1-1-11111-1-1-10000-1-11111
χ293333333-1-1333333-1-1-1-1-10000-3-3-1-1-1-1-1-10000000000000000-3111-11-1-1-11111-100001-1-1-111
χ303333333-1-1333333-1-1-1-1-10000-3-3-1-1-1-1-1-10000000000000000-311-11-1111-1-11-110000-1111-1-1
χ3133-33333-1-13-3-33-3-31-1-1-1-100003311-1-1110000000000000000-3-1-111-1-1-11-111110000-1-1-11-11
χ3233-33333-1-13-3-33-3-31-1-1-1-100003311-1-1110000000000000000-3-1-1-1-1111-11-11-1-10000111-11-1
χ3333-33333-1-13-3-33-3-31-1-1-1-10000-3-311-1-11100000000000000003111-1-11-111-1-11-10000-11-111-1
χ3433-33333-1-13-3-33-3-31-1-1-1-10000-3-311-1-1110000000000000000311-111-11-1-11-1-1100001-11-1-11
χ354444-24-244-24-2-2-2-2444-2-2-2-2-2-2004-2-2-2-2-2-2111-2111-2-2111111000000000000000000000000
χ36444-24-2444-2-24-2-2-24-2-244-2-2-2-200-24-2-2-2-21-2111-21111-2-21111000000000000000000000000
χ37444-2-2-2-2441-2-21114-2-2-2-2444400-2-21111-2-211-2-211-2-2-2-21111000000000000000000000000
χ38444-2-2-2-2441-2-21114-2-2-2-2-2-2-2-200-2-2111111−1+3i32−1−3i3211−1+3i32−1−3i321111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000
χ39444-2-2-2-2441-2-21114-2-2-2-2-2-2-2-200-2-2111111−1−3i32−1+3i3211−1−3i32−1+3i321111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000
χ4044-44-24-244-2-42-222-444-2-2-2-22200-42-2-222-2111-211122-1-1-1-1-1-1000000000000000000000000
χ4144-4-24-2444-22-4-222-4-2-244-2-222002-4-2-2221-2111-211-1-122-1-1-1-1000000000000000000000000
χ4244-4-2-2-2-2441221-1-1-4-2-2-2-244-4-4002211-1-1-2-211-2-2112222-1-1-1-1000000000000000000000000
χ4344-4-2-2-2-2441221-1-1-4-2-2-2-2-2-222002211-1-111−1+3i32−1−3i3211−1+3i32−1−3i32-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000
χ4444-4-2-2-2-2441221-1-1-4-2-2-2-2-2-222002211-1-111−1−3i32−1+3i3211−1−3i32−1+3i32-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000
χ454-404-2-424-4-20020004-4-224-4000000-22004-2-2-2-422200000000000000000000000000000000
χ464-404-2-424-4-20020004-4-22-222i3−2i30000-2200-21112-1-1-12i3−2i3−i3i3−i3−i3i3i3000000000000000000000000
χ474-404-2-424-4-20020004-4-22-22−2i32i30000-2200-21112-1-1-1−2i32i3i3−i3i3i3−i3−i3000000000000000000000000
χ484-40-242-44-4-2002000-224-44-4000000-2200-24-2-22-42200000000000000000000000000000000
χ494-40-242-44-4-2002000-224-4-222i3−2i30000-22001-211-12-1-1−i3i32i3−2i3−i3−i3i3i3000000000000000000000000
χ504-40-242-44-4-2002000-224-4-22−2i32i30000-22001-211-12-1-1i3−i3−2i32i3i3i3−i3−i3000000000000000000000000
χ514-40-2-2224-4100-13-30-22-224-40000001-13-3-2-21122-1-100003-3-33000000000000000000000000
χ524-40-2-2224-4100-13-30-22-22-222i3−2i300001-13-311−1+3i32−1−3i32-1-11−3i321+3i32−i3i3−i3i3−3+i323+i323−i32−3−i32000000000000000000000000
χ534-40-2-2224-4100-13-30-22-22-22−2i32i300001-13-311−1−3i32−1+3i32-1-11+3i321−3i32i3−i3i3−i3−3−i323−i323+i32−3+i32000000000000000000000000
χ544-40-2-2224-4100-1-330-22-224-40000001-1-33-2-21122-1-10000-333-3000000000000000000000000
χ554-40-2-2224-4100-1-330-22-22-222i3−2i300001-1-3311−1−3i32−1+3i32-1-11+3i321−3i32−i3i3−i3i33+i32−3+i32−3−i323−i32000000000000000000000000
χ564-40-2-2224-4100-1-330-22-22-22−2i32i300001-1-3311−1+3i32−1−3i32-1-11−3i321+3i32i3−i3i3−i33−i32−3−i32−3+i323+i32000000000000000000000000
χ576666-36-3-2-2-36-3-3-3-3-2-2-211000000-2111110000000000000000000020200-2-200-100000-10011
χ586666-36-3-2-2-36-3-3-3-3-2-2-211000000-21111100000000000000000000-20-2002200100000100-1-1
χ59666-36-36-2-2-3-36-3-3-3-211-2-20000001-2111100000000000000000002020-2-2000-100000-101100
χ60666-36-36-2-2-3-36-3-3-3-211-2-20000001-211110000000000000000000-20-202200010000010-1-100
χ6166-66-36-3-2-2-3-63-3332-2-2110000002-111-1-10000000000000000000020-200-2200-1000001001-1
χ6266-66-36-3-2-2-3-63-3332-2-2110000002-111-1-100000000000000000000-202002-200100000-100-11
χ6366-6-36-36-2-2-33-6-333211-2-2000000-1211-1-1000000000000000000020-20-22000-100000101-100
χ6466-6-36-36-2-2-33-6-333211-2-2000000-1211-1-10000000000000000000-20202-2000100000-10-1100
χ656-6066-6-6-22600-6000-22-2200006-600-220000000000000000000-22000000000000000000000
χ666-6066-6-6-22600-6000-22-220000-6600-2200000000000000000002-2000000000000000000000
χ67121212-6-6-6-6-4-43-6-6333-4222200000022-1-1-1-10000000000000000000000000000000000000000
χ681212-12-6-6-6-6-4-43663-3-342222000000-2-2-1-1110000000000000000000000000000000000000000
χ6912-12012-6-126-44-6006000-442-2000000002-2000000000000000000000000000000000000000000
χ7012-120-6126-12-44-60060002-2-44000000002-2000000000000000000000000000000000000000000
χ7112-120-6-666-44300-39-902-22-200000000-11-330000000000000000000000000000000000000000
χ7212-120-6-666-44300-3-9902-22-200000000-113-30000000000000000000000000000000000000000

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