Finite Group Databasebeta

← Group #13165964

Character table — Group #13165964

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222222222222266666688889999121212121212121212121212121212121212121212121212121216161616161616161616161616161616242424242424242454545454545472727272108108
order122233336666666666664488883666444444121212121212121224242424242424242424242424242424333366666666666612121212121212124488881212121222
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ41111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511-1-11111-1-1-1-11111-1-1-1-1-11ii−i−i11-1-1ii−i−ii−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−ii−i11-1-1ii−i−i1-1
χ611-1-11111-1-1-1-11111-1-1-1-1-11ii−i−i11-1-1−i−iiii−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i−ii-1-111−i−iii-11
χ711-1-11111-1-1-1-11111-1-1-1-1-11−i−iii11-1-1ii−i−i−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiiii−i-1-111ii−i−i-11
χ811-1-11111-1-1-1-11111-1-1-1-1-11−i−iii11-1-1−i−iii−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−ii11-1-1−i−iii1-1
χ922222222222222222222220000-1-1-1-1222200222222220000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000220000-1-1-1-100
χ1022222222222222222222220000-1-1-1-1-2-2-2-200222222220000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-20000111100
χ1122222-1-1-12-1-1-12-1-1-12-1-1-122222222220000222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-12-1-1-12-1-1-1000000000000
χ1222222-1-1-12-1-1-12-1-1-12-1-1-122-2-2-2-222220000-2-22-1-1-12-1-1-1-2-2111111-2-21111112-1-1-12-1-1-122-1-1-1-1-1-1-2111-2111000000000000
χ132222-12-1-1-12-1-1-12-1-1-12-1-12222222222000022-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1-12-1-1-12-1-1000000000000
χ142222-12-1-1-12-1-1-12-1-1-12-1-122-2-2-2-222220000-2-2-12-1-1-12-1-111-2-2111111-2-21111-12-1-1-12-1-1-1-122-1-1-1-11-2111-211000000000000
χ152222-1-12-1-1-12-1-1-12-1-1-12-12222222222000022-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-12-1-1-12-1-1-1-1-122-1-1-1-12-1-1-12-1000000000000
χ162222-1-12-1-1-12-1-1-12-1-1-12-122-2-2-2-222220000-2-2-1-12-1-1-12-11111-2-2111111-2-211-1-12-1-1-12-1-1-1-1-122-1-111-2111-21000000000000
χ172222-1-1-12-1-1-12-1-1-12-1-1-122222222222000022-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-12-1-1-12-1-1-1-1-1-122-1-1-12-1-1-12000000000000
χ182222-1-1-12-1-1-12-1-1-12-1-1-1222-2-2-2-222220000-2-2-1-1-12-1-1-12111111-2-2111111-2-2-1-1-12-1-1-12-1-1-1-1-1-122111-2111-2000000000000
χ1922-2-22222-2-2-2-22222-2-2-2-2-220000-1-1112i2i−2i−2i002222-2-2-2-20000000000000000-1-1-1-1-1-1-1-111111111000000002i−2i0000−i−iii00
χ2022-2-22222-2-2-2-22222-2-2-2-2-220000-1-111−2i−2i2i2i002222-2-2-2-20000000000000000-1-1-1-1-1-1-1-11111111100000000−2i2i0000ii−i−i00
χ2122-2-22-1-1-1-21112-1-1-1-2111-222i2i−2i−2i22-2-200002i−2i2-1-1-1-21112i2i−i−i−i−i−i−i−2i−2iiiiiii2-1-1-12-1-1-1-2-21111112i−i−i−i−2iiii000000000000
χ2222-2-22-1-1-1-21112-1-1-1-2111-22−2i−2i2i2i22-2-20000−2i2i2-1-1-1-2111−2i−2iiiiiii2i2i−i−i−i−i−i−i2-1-1-12-1-1-1-2-2111111−2iiii2i−i−i−i000000000000
χ2322-2-2-12-1-11-211-12-1-11-211-222i2i−2i−2i22-2-200002i−2i-12-1-11-211−i−i2i2i−i−i−i−iii−2i−2iiiii-12-1-1-12-1-111-2-21111−i2i−i−ii−2iii000000000000
χ2422-2-2-12-1-11-211-12-1-11-211-22−2i−2i2i2i22-2-20000−2i2i-12-1-11-211ii−2i−2iiiii−i−i2i2i−i−i−i−i-12-1-1-12-1-111-2-21111i−2iii−i2i−i−i000000000000
χ2522-2-2-1-12-111-21-1-12-111-21-222i2i−2i−2i22-2-200002i−2i-1-12-111-21−i−i−i−i2i2i−i−iiiii−2i−2iii-1-12-1-1-12-11111-2-211−i−i2i−iii−2ii000000000000
χ2622-2-2-1-12-111-21-1-12-111-21-22−2i−2i2i2i22-2-20000−2i2i-1-12-111-21iiii−2i−2iii−i−i−i−i2i2i−i−i-1-12-1-1-12-11111-2-211ii−2ii−i−i2i−i000000000000
χ2722-2-2-1-1-12111-2-1-1-12111-2-222i2i−2i−2i22-2-200002i−2i-1-1-12111-2−i−i−i−i−i−i2i2iiiiiii−2i−2i-1-1-12-1-1-12111111-2-2−i−i−i2iiii−2i000000000000
χ2822-2-2-1-1-12111-2-1-1-12111-2-22−2i−2i2i2i22-2-20000−2i2i-1-1-12111-2iiiiii−2i−2i−i−i−i−i−i−i2i2i-1-1-12-1-1-12111111-2-2iii−2i−i−i−i2i000000000000
χ292-22-22222-2-2-2-2-2-2-2-2222200i2−i2i2−i2-111-12-22-20000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2-1-1-1-111111-11-11-11-10000000000i2−i2i2−i21-11-100
χ302-22-22222-2-2-2-2-2-2-2-2222200i2−i2i2−i2-111-1-22-220000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2-1-1-1-111111-11-11-11-10000000000−i2i2−i2i2-11-1100
χ312-22-22222-2-2-2-2-2-2-2-2222200−i2i2−i2i2-111-12-22-20000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2-1-1-1-111111-11-11-11-10000000000−i2i2−i2i21-11-100
χ322-22-22222-2-2-2-2-2-2-2-2222200−i2i2−i2i2-111-1-22-220000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2-1-1-1-111111-11-11-11-10000000000i2−i2i2−i2-11-1100
χ332-2-2222222222-2-2-2-2-2-2-2-2002−2−22-11-112i−2i−2i2i00000000002−22−22−22−2−22−22−22−22-1-1-1-11111-11-11-11-110000000000−i2i2i2−i2i−i−ii00
χ342-2-2222222222-2-2-2-2-2-2-2-2002−2−22-11-11−2i2i2i−2i00000000002−22−22−22−2−22−22−22−22-1-1-1-11111-11-11-11-110000000000i2−i2−i2i2−iii−i00
χ352-2-2222222222-2-2-2-2-2-2-2-200−222−2-11-112i−2i−2i2i0000000000−22−22−22−222−22−22−22−2-1-1-1-11111-11-11-11-110000000000i2−i2−i2i2i−i−ii00
χ362-2-2222222222-2-2-2-2-2-2-2-200−222−2-11-11−2i2i2i−2i0000000000−22−22−22−222−22−22−22−2-1-1-1-11111-11-11-11-110000000000−i2i2i2−i2−iii−i00
χ3733333333333333333333-1-1111100003333-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-1-1-1-1-1-1-1-1-1-111110000-1-1
χ3833333333333333333333-1-111110000-3-3-3-3-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-1-1-1-1-1-1-1-111-1-1-1-1000011
χ3933333333333333333333-1-1-1-1-1-10000333311-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000011111111-1-1-1-1-1-1000011
χ4033333333333333333333-1-1-1-1-1-10000-3-3-3-311-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000111111111111110000-1-1
χ4133-3-33333-3-3-3-33333-3-3-3-31-1ii−i−i00003i3i−3i−3i−ii-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i0000000000000000−i−i−i−iiiii−ii11-1-10000-11
χ4233-3-33333-3-3-3-33333-3-3-3-31-1ii−i−i0000−3i−3i3i3i−ii-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i0000000000000000−i−i−i−iiiiii−i-1-11100001-1
χ4333-3-33333-3-3-3-33333-3-3-3-31-1−i−iii00003i3i−3i−3ii−i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii0000000000000000iiii−i−i−i−i−ii-1-11100001-1
χ4433-3-33333-3-3-3-33333-3-3-3-31-1−i−iii0000−3i−3i3i3ii−i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii0000000000000000iiii−i−i−i−ii−i11-1-10000-11
χ4544444-2-2-24-2-2-24-2-2-24-2-2-2440000-2-2-2-20000004-2-2-24-2-2-20000000000000000-2111-2111-2-211111100000000000000000000
χ464444-24-2-2-24-2-2-24-2-2-24-2-2440000-2-2-2-2000000-24-2-2-24-2-200000000000000001-2111-21111-2-2111100000000000000000000
χ474444-2-24-2-2-24-2-2-24-2-2-24-2440000-2-2-2-2000000-2-24-2-2-24-2000000000000000011-2111-211111-2-21100000000000000000000
χ484444-2-2-24-2-2-24-2-2-24-2-2-24440000-2-2-2-2000000-2-2-24-2-2-240000000000000000111-2111-2111111-2-200000000000000000000
χ4944-4-44-2-2-2-42224-2-2-2-4222-440000-2-2220000004-2-2-2-42220000000000000000-2111-211122-1-1-1-1-1-100000000000000000000
χ5044-4-4-24-2-22-422-24-2-22-422-440000-2-222000000-24-2-22-42200000000000000001-2111-211-1-122-1-1-1-100000000000000000000
χ5144-4-4-2-24-222-42-2-24-222-42-440000-2-222000000-2-24-222-42000000000000000011-2111-21-1-1-1-122-1-100000000000000000000
χ5244-4-4-2-2-24222-4-2-2-24222-4-440000-2-222000000-2-2-24222-40000000000000000111-2111-2-1-1-1-1-1-12200000000000000000000
χ534-44-44444-4-4-4-4-4-4-4-444440000001-1-114-44-4000000000000000000000000001111-1-1-1-1-11-11-11-1100000000000000-11-1100
χ544-44-44444-4-4-4-4-4-4-4-444440000001-1-11-44-44000000000000000000000000001111-1-1-1-1-11-11-11-11000000000000001-11-100
χ554-44-44-2-2-2-4222-42224-2-2-2002i2−2i22i2−2i2-222-2000000000000002i2−2i2−i2i2−i2i2−i2i22i2−2i2−i2i2−i2i2−i2i2-21112-1-1-12-2-11-11-1100000000000000000000
χ564-44-44-2-2-2-4222-42224-2-2-200−2i22i2−2i22i2-222-200000000000000−2i22i2i2−i2i2−i2i2−i2−2i22i2i2−i2i2−i2i2−i2-21112-1-1-12-2-11-11-1100000000000000000000
χ574-44-4-24-2-22-4222-422-24-2-2002i2−2i22i2−2i2-222-200000000000000−i2i22i2−2i2−i2i2−i2i2−i2i22i2−2i2−i2i2−i2i21-211-12-1-1-112-2-11-1100000000000000000000
χ584-44-4-24-2-22-4222-422-24-2-200−2i22i2−2i22i2-222-200000000000000i2−i2−2i22i2i2−i2i2−i2i2−i2−2i22i2i2−i2i2−i21-211-12-1-1-112-2-11-1100000000000000000000
χ594-44-4-2-24-222-4222-42-2-24-2002i2−2i22i2−2i2-222-200000000000000−i2i2−i2i22i2−2i2−i2i2−i2i2−i2i22i2−2i2−i2i211-21-1-12-1-11-112-2-1100000000000000000000
χ604-44-4-2-24-222-4222-42-2-24-200−2i22i2−2i22i2-222-200000000000000i2−i2i2−i2−2i22i2i2−i2i2−i2i2−i2−2i22i2i2−i211-21-1-12-1-11-112-2-1100000000000000000000
χ614-44-4-2-2-24222-4222-4-2-2-24002i2−2i22i2−2i2-222-200000000000000−i2i2−i2i2−i2i22i2−2i2−i2i2−i2i2−i2i22i2−2i2111-2-1-1-12-11-11-112-200000000000000000000
χ624-44-4-2-2-24222-4222-4-2-2-2400−2i22i2−2i22i2-222-200000000000000i2−i2i2−i2i2−i2−2i22i2i2−i2i2−i2i2−i2−2i22i2111-2-1-1-12-11-11-112-200000000000000000000
χ634-4-4444444444-4-4-4-4-4-4-4-40000001-11-14i−4i−4i4i000000000000000000000000001111-1-1-1-11-11-11-11-100000000000000−iii−i00
χ644-4-4444444444-4-4-4-4-4-4-4-40000001-11-1−4i4i4i−4i000000000000000000000000001111-1-1-1-11-11-11-11-100000000000000i−i−ii00
χ654-4-444-2-2-24-2-2-2-4222-42220022−22−2222-22-220000000000000022−22−22−22−22−22222−22−22−2-21112-1-1-1-221-11-11-100000000000000000000
χ664-4-444-2-2-24-2-2-2-4222-422200−222222−22-22-2200000000000000−22222−22−22−222−22−22−22−22-21112-1-1-1-221-11-11-100000000000000000000
χ674-4-44-24-2-2-24-2-22-4222-4220022−22−2222-22-2200000000000000−2222−22−22−222−2−22222−22−21-211-12-1-11-1-221-11-100000000000000000000
χ684-4-44-24-2-2-24-2-22-4222-42200−222222−22-22-22000000000000002−2−22222−22−2−2222−22−22−221-211-12-1-11-1-221-11-100000000000000000000
χ694-4-44-2-24-2-2-24-222-4222-420022−22−2222-22-2200000000000000−22−2222−22−222−22−2−22222−211-21-1-12-11-11-1-221-100000000000000000000
χ704-4-44-2-24-2-2-24-222-4222-4200−222222−22-22-22000000000000002−22−2−22222−2−22−2222−22−2211-21-1-12-11-11-1-221-100000000000000000000
χ714-4-44-2-2-24-2-2-24222-4222-40022−22−2222-22-2200000000000000−22−22−2222−222−22−22−2−2222111-2-1-1-121-11-11-1-2200000000000000000000
χ724-4-44-2-2-24-2-2-24222-4222-400−222222−22-22-22000000000000002−22−22−2−2222−22−22−2222−22111-2-1-1-121-11-11-1-2200000000000000000000
χ7366666-3-3-36-3-3-36-3-3-36-3-3-3-2-2222200000000-2-2-2111-211122-1-1-1-1-1-122-1-1-1-1-1-10000000000000000-2111-2111000000000000
χ7466666-3-3-36-3-3-36-3-3-36-3-3-3-2-2-2-2-2-20000000022-2111-2111-2-2111111-2-211111100000000000000002-1-1-12-1-1-1000000000000
χ756666-36-3-3-36-3-3-36-3-3-36-3-3-2-2222200000000-2-21-2111-211-1-122-1-1-1-1-1-122-1-1-1-100000000000000001-2111-211000000000000
χ766666-36-3-3-36-3-3-36-3-3-36-3-3-2-2-2-2-2-200000000221-2111-21111-2-2111111-2-211110000000000000000-12-1-1-12-1-1000000000000
χ776666-3-36-3-3-36-3-3-36-3-3-36-3-2-2222200000000-2-211-2111-21-1-1-1-122-1-1-1-1-1-122-1-1000000000000000011-2111-21000000000000
χ786666-3-36-3-3-36-3-3-36-3-3-36-3-2-2-2-2-2-2000000002211-2111-211111-2-2111111-2-2110000000000000000-1-12-1-1-12-1000000000000
χ796666-3-3-36-3-3-36-3-3-36-3-3-36-2-2222200000000-2-2111-2111-2-1-1-1-1-1-122-1-1-1-1-1-1220000000000000000111-2111-2000000000000
χ806666-3-3-36-3-3-36-3-3-36-3-3-36-2-2-2-2-2-20000000022111-2111-2111111-2-2111111-2-20000000000000000-1-1-12-1-1-12000000000000
χ8166-6-66-3-3-3-63336-3-3-3-63332-22i2i−2i−2i00000000−2i2i-21112-1-1-12i2i−i−i−i−i−i−i−2i−2iiiiiii0000000000000000−2iiii2i−i−i−i000000000000
χ8266-6-66-3-3-3-63336-3-3-3-63332-2−2i−2i2i2i000000002i−2i-21112-1-1-1−2i−2iiiiiii2i2i−i−i−i−i−i−i00000000000000002i−i−i−i−2iiii000000000000
χ8366-6-6-36-3-33-633-36-3-33-6332-22i2i−2i−2i00000000−2i2i1-211-12-1-1−i−i2i2i−i−i−i−iii−2i−2iiiii0000000000000000i−2iii−i2i−i−i000000000000
χ8466-6-6-36-3-33-633-36-3-33-6332-2−2i−2i2i2i000000002i−2i1-211-12-1-1ii−2i−2iiiii−i−i2i2i−i−i−i−i0000000000000000−i2i−i−ii−2iii000000000000
χ8566-6-6-3-36-333-63-3-36-333-632-22i2i−2i−2i00000000−2i2i11-21-1-12-1−i−i−i−i2i2i−i−iiiii−2i−2iii0000000000000000ii−2ii−i−i2i−i000000000000
χ8666-6-6-3-36-333-63-3-36-333-632-2−2i−2i2i2i000000002i−2i11-21-1-12-1iiii−2i−2iii−i−i−i−i2i2i−i−i0000000000000000−i−i2i−iii−2ii000000000000
χ8766-6-6-3-3-36333-6-3-3-36333-62-22i2i−2i−2i00000000−2i2i111-2-1-1-12−i−i−i−i−i−i2i2iiiiiii−2i−2i0000000000000000iii−2i−i−i−i2i000000000000
χ8866-6-6-3-3-36333-6-3-3-36333-62-2−2i−2i2i2i000000002i−2i111-2-1-1-12iiiiii−2i−2i−i−i−i−i−i−i2i2i0000000000000000−i−i−i2iiii−2i000000000000
χ898-88-88-4-4-4-8444-84448-4-4-40000002-2-220000000000000000000000000000002-1-1-1-2111-221-11-11-100000000000000000000
χ908-88-8-48-4-44-8444-844-48-4-40000002-2-22000000000000000000000000000000-12-1-11-2111-1-221-11-100000000000000000000
χ918-88-8-4-48-444-8444-84-4-48-40000002-2-22000000000000000000000000000000-1-12-111-211-11-1-221-100000000000000000000
χ928-88-8-4-4-48444-8444-8-4-4-480000002-2-22000000000000000000000000000000-1-1-12111-21-11-11-1-2200000000000000000000
χ938-8-888-4-4-48-4-4-4-8444-84440000002-22-20000000000000000000000000000002-1-1-1-21112-2-11-11-1100000000000000000000
χ948-8-88-48-4-4-48-4-44-8444-8440000002-22-2000000000000000000000000000000-12-1-11-211-112-2-11-1100000000000000000000
χ958-8-88-4-48-4-4-48-444-8444-840000002-22-2000000000000000000000000000000-1-12-111-21-11-112-2-1100000000000000000000
χ968-8-88-4-4-48-4-4-48444-8444-80000002-22-2000000000000000000000000000000-1-1-12111-2-11-11-112-200000000000000000000

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