Finite Group Databasebeta

← Group #13165300

Character table — Group #13165300

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size112224444444668888888121212121212121212121618182424242424242424242424363636363636363648484872727272108144216
order123463366121212883366121212882424242424242424122441212242424242424242424666121212121212282424868
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-11111111111111111-1-1-1-1-1-1-11-1-1
χ3111111111111111111111-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-11-1-1-1-111111-1-1-111-1
χ4111111111111111111111-1-11111-1-1-1-1111-1-1-1-1-111-1-1-1-1-1-11-1-1-1-11-1-1-1-11111-11
χ5111111111111-1-1111111111-1-1-1-1111111111111-1-11111-1-11-1-1-1-11111-1111-1-1-1
χ6111111111111-1-1111111111-1-1-1-11111111-1-1-111-1-11111-1-11-1-1-1-11-1-1-11-1-1-1-111
χ7111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-11
χ8111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-11-1
χ922222222222222222222200222200002-2-20000022000000-20000-20000000-200
χ10222222222222-2-2222222200-2-2-2-200002-2-200000-2-2000000-20000-20000000200
χ11222-222222-2-2-2002222-2-2-20000000000-2-22000000000002-2-222-2-220000000000
χ12222-222222-2-2-2002222-2-2-20000000000-2-2200000000000-22-2-2-22220000000000
χ13222-222222-2-2-2002222-2-2-22i−2i00002i2i−2i−2i-22-20002i−2i002i2i−2i−2i0020000-20000000000
χ14222-222222-2-2-2002222-2-2-2−2i2i0000−2i−2i2i2i-22-2000−2i2i00−2i−2i2i2i0020000-20000000000
χ1522-12-12222-12200-1-1-1-12-1-12200002222-1222-1-1-1-100-1-1-1-100-10000-12-1-102-1-1000
χ1622-12-12222-12200-1-1-1-12-1-12200002222-122-211-1-100-1-1-1-100-10000-1-2110-211000
χ1722-12-12222-12200-1-1-1-12-1-1-2-20000-2-2-2-2-1222-1-11100111100-10000-12-1-10-211000
χ1822-12-12222-12200-1-1-1-12-1-1-2-20000-2-2-2-2-122-2111100111100-10000-1-21102-1-1000
χ1922-1-2-122221-2-200-1-1-1-1-2112i−2i00002i2i−2i−2i12-20−i3i3−ii00−i−iii00-1000010−i3i3003−3000
χ2022-1-2-122221-2-200-1-1-1-1-2112i−2i00002i2i−2i−2i12-20i3−i3−ii00−i−iii00-1000010i3−i300−33000
χ2122-1-2-122221-2-200-1-1-1-1-211−2i2i0000−2i−2i2i2i12-20−i3i3i−i00ii−i−i00-1000010−i3i300−33000
χ2222-1-2-122221-2-200-1-1-1-1-211−2i2i0000−2i−2i2i2i12-20i3−i3i−i00ii−i−i00-1000010i3−i3003−3000
χ23444441-2-21411441-21-2-211221111-1-1-1-1-20000022-2-2-1-1-1-1220-1-1-1-100000000000
χ24444441-2-21411441-21-2-211-2-211111111-200000-2-2-2-21111-2-20111100000000000
χ25444441-2-21411-4-41-21-2-21122-1-1-1-1-1-1-1-1-2000002222-1-1-1-1-2-20111100000000000
χ26444441-2-21411-4-41-21-2-211-2-2-1-1-1-11111-200000-2-2221111220-1-1-1-100000000000
χ2744444-211-24-2-244-21-211-2-200-2-2-2-200001002220011000000000000-1-1-120000-10
χ2844444-211-24-2-244-21-211-2-200-2-2-2-20000100-2-2-20011000000000000111-2000010
χ2944444-211-24-2-2-4-4-21-211-2-2002222000010022200-1-1000000000000-1-1-1-2000010
χ3044444-211-24-2-2-4-4-21-211-2-20022220000100-2-2-200-1-100000000000011120000-10
χ31444-441-2-21-4-1-1001-21-22-1-12i−2i3i3i−3i−3i−i−iii2000002i−2i00−i−iii2-20-1-11100000000000
χ32444-441-2-21-4-1-1001-21-22-1-12i−2i−3i−3i3i3i−i−iii2000002i−2i00−i−iii-22011-1-100000000000
χ33444-441-2-21-4-1-1001-21-22-1-1−2i2i3i3i−3i−3iii−i−i200000−2i2i00ii−i−i-22011-1-100000000000
χ34444-441-2-21-4-1-1001-21-22-1-1−2i2i−3i−3i3i3iii−i−i200000−2i2i00ii−i−i2-20-1-11100000000000
χ3544-24-24444-24400-2-2-2-24-2-20000000000-2-4-400000000000002000020000000000
χ3644-2-4-244442-4-400-2-2-2-2-42200000000002-44000000000000020000-20000000000
χ374-440-41-22-103i−3i−2i22i21-2-1203i−3i00−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000−i2i2−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000−i3i33−300000000000
χ384-440-41-22-103i−3i−2i22i21-2-1203i−3i00−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000−i2i2ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000i3−i3−3300000000000
χ394-440-41-22-103i−3i2i2−2i21-2-1203i−3i00ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000i2−i2−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000i3−i3−3300000000000
χ404-440-41-22-103i−3i2i2−2i21-2-1203i−3i00ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000i2−i2ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000−i3i33−300000000000
χ414-440-41-22-10−3i3i−2i22i21-2-120−3i3i002ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000−i2i2ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000−i3i3−3300000000000
χ424-440-41-22-10−3i3i−2i22i21-2-120−3i3i002ζ5−ζ7+2ζ13−ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000−i2i2−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000i3−i33−300000000000
χ434-440-41-22-10−3i3i2i2−2i21-2-120−3i3i00−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000i2−i2ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000i3−i33−300000000000
χ444-440-41-22-10−3i3i2i2−2i21-2-120−3i3i00−2ζ5+ζ7−2ζ13+ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000i2−i2−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000−i3i3−3300000000000
χ454-440-444-4-4000−2i22i244-4-4000002i2−2i2−2i22i20000000000002i2−2i20000000000000000000000
χ464-440-444-4-40002i2−2i244-4-400000−2i22i22i2−2i2000000000000−2i22i20000000000000000000000
χ47888-88-422-4-84400-42-42-2440000000000-20000000000000000000000000000000
χ4888-48-42-4-42-42200-12-12-4-1-1440000-2-2-2-2200000-2-2001111000000000000000000
χ4988-48-42-4-42-42200-12-12-4-1-1-4-4000022222000002200-1-1-1-1000000000000000000
χ5088-48-4-422-4-4-4-4002-12-12220000000000-1004-2-20000000000000000-2110000000
χ5188-48-4-422-4-4-4-4002-12-12220000000000-100-42200000000000000002-1-10000000
χ5288-4-8-42-4-424-2-200-12-124114i−4i0000−2i−2i2i2i-200000−2i2i00ii−i−i000000000000000000
χ5388-4-8-42-4-424-2-200-12-12411−4i4i00002i2i−2i−2i-2000002i−2i00−i−iii000000000000000000
χ5488-4-8-4-422-4444002-12-1-2-2-200000000001000−2i32i300000000000000000i3−i30000000
χ5588-4-8-4-422-4444002-12-1-2-2-2000000000010002i3−2i300000000000000000−i3i30000000
χ568-880-8-42-24000−4i24i2-424-200000−2i22i22i2−2i2000000000000i2−i20000000000000000000000
χ578-880-8-42-240004i2−4i2-424-2000002i2−2i2−2i22i2000000000000−i2i20000000000000000000000
χ588-8-4042-44-206i−6i00-121-20−3i3i000000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ130000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000
χ598-8-4042-44-206i−6i00-121-20−3i3i0000002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ130000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000
χ608-8-4042-44-20−6i6i00-121-203i−3i0000002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ230000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000
χ618-8-4042-44-20−6i6i00-121-203i−3i000000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ230000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000
χ628-8-40488-8-800000-4-444000000000000000000000000000000000000000000000
χ6316-16-808-84-48000004-2-42000000000000000000000000000000000000000000000

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