Finite Group Databasebeta

← Group #13138039

Character table — Group #13138039

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size1111222222444466666666881212121212121212121212121818181818182424242424242424363636363636363636363636363636363636363636727272727272
order122234466644121233666666121236661212121212121212441212121212121212121212124448888121212121212242424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-111
χ4111111111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-111-1-1
χ51111111111-1-11111111111-1-111111-1-1-1-1111111111-1-111-1-1-1-11-1-1111111-1-1-1-111111111-1-1-1-1-1-1
χ61111111111-1-11111111111-1-111111-1-1-1-1111111111-1-111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111-1-11111111111-1-111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-111-1-1
χ81111111111-1-11111111111-1-111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-111-1-11111-1-1-1-11111-11-1-111
χ9222222222222222-1-1-1-122222-1-1-1-1-1222222-1000000-1-1-1-1-1-1-1-100000220000000000-1-1-1-120-1-100
χ10222222222222222-1-1-1-122222-1-1-1-1-1222222-1000000-1-1-1-1-1-1-1-100000-2-200000000001111-201100
χ1122222222222222-12222-1-1-122-1-1-1-12-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-12220000-1-1-1-1-1-100000000000000
χ1222222222222222-12222-1-1-122-1-1-1-12-1-1-1-1-1-12-2-2111122-1-1-1-1-1-1-2-2-2000011111100000000000000
χ132222222222-2-2222-1-1-1-1222-2-2-1-1-1-1-1-2-2-2-222-100000011-1-1111100000220000000000-1-1-1-1-201100
χ142222222222-2-2222-1-1-1-1222-2-2-1-1-1-1-1-2-2-2-222-100000011-1-1111100000-2-20000000000111120-1-100
χ152222222222-2-222-12222-1-1-1-2-2-1-1-1-121111-1-1222-1-1-1-1-2-2-1-111112-2-20000-1-1111100000000000000
χ162222222222-2-222-12222-1-1-1-2-2-1-1-1-121111-1-12-2-21111-2-2-1-11111-222000011-1-1-1-100000000000000
χ1722222-2-222200-2-222222222002222-20000-2-2-222222200-2-20000-2000000-2-2000000000000000000
χ1822222-2-222200-2-222222222002222-20000-2-2-2-2-2-2-2-2-200-2-20000200000022000000000000000000
χ1922222-2-222200-2-2-12222-1-1-100-1-1-1-1-2−i3−i3i3i311-222-1-1-1-10011−i3−i3i3i3-200000011−i3−i3i3i300000000000000
χ2022222-2-222200-2-2-12222-1-1-100-1-1-1-1-2−i3−i3i3i311-2-2-211110011−i3−i3i3i32000000-1-1i3i3−i3−i300000000000000
χ2122222-2-222200-2-2-12222-1-1-100-1-1-1-1-2i3i3−i3−i311-222-1-1-1-10011i3i3−i3−i3-200000011i3i3−i3−i300000000000000
χ2222222-2-222200-2-2-12222-1-1-100-1-1-1-1-2i3i3−i3−i311-2-2-211110011i3i3−i3−i32000000-1-1−i3−i3i3i300000000000000
χ232-22-2200-22-2000022-2-22-22-2002-2-22000000002i−2i2i2i−2i−2i00000000000−i2i22−2000000−i2−i2i2i222−2−2000000
χ242-22-2200-22-2000022-2-22-22-2002-2-22000000002i−2i2i2i−2i−2i00000000000i2−i2−22000000i2i2−i2−i2−2−222000000
χ252-22-2200-22-2000022-2-22-22-2002-2-2200000000−2i2i−2i−2i2i2i00000000000−i2i2−22000000−i2−i2i2i2−2−222000000
χ262-22-2200-22-2000022-2-22-22-2002-2-2200000000−2i2i−2i−2i2i2i00000000000i2−i22−2000000i2i2−i2−i222−2−2000000
χ272-2-2222-2-2-222i−2i2-222-22-2-2-222i−2i2-22-222i−2i2i−2i2-2-20000002i−2i2-22i−2i2i−2i000000000000000000000000000
χ282-2-2222-2-2-222i−2i2-22-11-11-2-222i−2i-11-11-12i−2i2i−2i2-21000000−ii-11−ii−ii000000000000000003−33−300−i3i300
χ292-2-2222-2-2-222i−2i2-22-11-11-2-222i−2i-11-11-12i−2i2i−2i2-21000000−ii-11−ii−ii00000000000000000−33−3300i3−i300
χ302-2-2222-2-2-222i−2i2-2-12-22-211-12i−2i-11-112−ii−ii-11-2003−33−32i−2i-11−ii−ii00000003−3−i3i3−i3i300000000000000
χ312-2-2222-2-2-222i−2i2-2-12-22-211-12i−2i-11-112−ii−ii-11-200−33−332i−2i-11−ii−ii0000000−33i3−i3i3−i300000000000000
χ322-2-2222-2-2-22−2i2i2-222-22-2-2-22−2i2i2-22-22−2i2i−2i2i2-2-2000000−2i2i2-2−2i2i−2i2i000000000000000000000000000
χ332-2-2222-2-2-22−2i2i2-22-11-11-2-22−2i2i-11-11-1−2i2i−2i2i2-21000000i−i-11i−ii−i000000000000000003−33−300i3−i300
χ342-2-2222-2-2-22−2i2i2-22-11-11-2-22−2i2i-11-11-1−2i2i−2i2i2-21000000i−i-11i−ii−i00000000000000000−33−3300−i3i300
χ352-2-2222-2-2-22−2i2i2-2-12-22-211-1−2i2i-11-112i−ii−i-11-2003−33−3−2i2i-11i−ii−i00000003−3i3−i3i3−i300000000000000
χ362-2-2222-2-2-22−2i2i2-2-12-22-211-1−2i2i-11-112i−ii−i-11-200−33−33−2i2i-11i−ii−i0000000−33−i3i3−i3i300000000000000
χ372-2-222-22-2-2200-2222-22-2-2-22002-22-2-20000-22200000000-22000002-20000002-2-2200000000000000
χ382-2-222-22-2-2200-2222-22-2-2-22002-22-2-20000-22200000000-2200000-22000000-222-200000000000000
χ392-2-222-22-2-2200-22-12-22-211-100-11-11-23−3−331-12003−33−3001-13−3−3302-20000−33-111-100000000000000
χ402-2-222-22-2-2200-22-12-22-211-100-11-11-23−3−331-1200−33−33001-13−3−330-2200003−31-1-1100000000000000
χ412-2-222-22-2-2200-22-12-22-211-100-11-11-2−333−31-12003−33−3001-1−333−30-220000−331-1-1100000000000000
χ422-2-222-22-2-2200-22-12-22-211-100-11-11-2−333−31-1200−33−33001-1−333−302-200003−3-111-100000000000000
χ4344444444444444-2-2-2-2-2-2-2-2441111-2-2-2-2-2-2-2-2000000-2-2111111000000000000000000000000000
χ444444444444-4-444-2-2-2-2-2-2-2-2-4-41111-22222-2-2-20000002211-1-1-1-1000000000000000000000000000
χ4544444-4-444400-4-44-2-2-2-244400-2-2-2-220000-4-4200000000220000000000000000000000000000000
χ4644444-4-444400-4-4-2-2-2-2-2-2-2-20011112−2i3−2i32i32i322200000000-1-1i3i3−i3−i3000000000000000000000000000
χ4744444-4-444400-4-4-2-2-2-2-2-2-2-200111122i32i3−2i3−2i322200000000-1-1−i3−i3i3i3000000000000000000000000000
χ4844-4-44004-4-40000444-4-44-4-40044-4-40000000000000000000000000000000000000000000000000
χ4944-4-44004-4-400004-2-2224-4-400-2-2220000000000000000000000000000000000000006−6−66000000
χ5044-4-44004-4-400004-2-2224-4-400-2-222000000000000000000000000000000000000000−666−6000000
χ5144-4-44004-4-40000-244-4-4-22200-2-2220000000000−2i32i32i3−2i300000000000000000000000000000000000
χ5244-4-44004-4-40000-244-4-4-22200-2-22200000000002i3−2i3−2i32i300000000000000000000000000000000000
χ534-44-4400-44-400004-222-2-44-400-222-200000000000000000000000000022−220000000000−2−222000000
χ544-44-4400-44-400004-222-2-44-400-222-2000000000000000000000000000−2222000000000022−2−2000000
χ554-44-4400-44-40000-24-4-442-2200-222-2000000004i−4i−2i−2i2i2i00000000000000000000000000000000000
χ564-44-4400-44-40000-24-4-442-2200-222-200000000−4i4i2i2i−2i−2i00000000000000000000000000000000000
χ574-4-4444-4-4-444i−4i4-4-2-22-2222-24i−4i1-11-1-2−2i2i−2i2i-222000000−2i2i1-1i−ii−i000000000000000000000000000
χ584-4-4444-4-4-44−4i4i4-4-2-22-2222-2−4i4i1-11-1-22i−2i2i−2i-2220000002i−2i1-1−ii−ii000000000000000000000000000
χ594-4-444-44-4-4400-444-22-22-4-4400-22-2220000-44-2000000002-20000000000000000000000000000000
χ604-4-444-44-4-4400-44-2-22-2222-2001-11-1223−23−23232-2-200000000-11−333−3000000000000000000000000000
χ614-4-444-44-4-4400-44-2-22-2222-2001-11-12−232323−232-2-200000000-113−3−33000000000000000000000000000
χ626666-366-3-3-366-3-300000000-3-3000000000000000000000000000002200000000-1-1-1-100000200-1-1
χ636666-366-3-3-366-3-300000000-3-300000000000000000000000000000-2-200000000111100000-20011
χ646666-366-3-3-3-6-6-3-30000000033000000000000000000000000000002200000000-1-1-1-100000-20011
χ656666-366-3-3-3-6-6-3-3000000003300000000000000000000000000000-2-200000000111100000200-1-1
χ666-6-66-36-633-36i−6i-3300000000−3i3i0000000000000000000000000000000000000003−33−300000000−i3i3
χ676-6-66-36-633-36i−6i-3300000000−3i3i000000000000000000000000000000000000000−33−3300000000i3−i3
χ686-6-66-36-633-3−6i6i-33000000003i−3i0000000000000000000000000000000000000003−33−300000000i3−i3
χ696-6-66-36-633-3−6i6i-33000000003i−3i000000000000000000000000000000000000000−33−3300000000−i3i3
χ7088-8-88008-8-80000-4-4-444-4440022-2-20000000000000000000000000000000000000000000000000
χ718-88-8800-88-80000-4-444-44-44002-2-220000000000000000000000000000000000000000000000000
χ7212121212-6-12-12-6-6-60066000000000000000000000000000000000000000000000000000000000000000
χ731212-12-12-600-66600000000000000000000000000000000000000000000000000000i6−i6−i6i60000000000
χ741212-12-12-600-66600000000000000000000000000000000000000000000000000000−i6i6i6−i60000000000
χ7512-1212-12-6006-660000000000000000000000000000000000000000000−2i22i200000000i2i2−i2−i20000000000
χ7612-1212-12-6006-6600000000000000000000000000000000000000000002i2−2i200000000−i2−i2i2i20000000000
χ7712-12-1212-6-121266-6006-6000000000000000000000000000000000000000000000000000000000000000

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