Finite Group Databasebeta

← Group #72252411

Character table — Group #72252411

Order 12288.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size112488121216242424242424484848484848486464646496969696969696128128192192192192192192192192192192192192192192192192192192192256256256384384512512512512512512768768768
order1222222242244442224444444422244443644444444444444488886668861212121212488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111-1-1-1-11111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1
χ3111111111111-1-111-1-111-111111-1-11-1-1-1-1111-1-1-1-111111-1-1-1-11-1-1-1-1111-1-1111111-1-1-1
χ4111111111111-1-111-1-111-11-1-1-1-1-1-11-1-1-1-111111111-1-1-1-111111-1-1-1-1111-1-111-1-1-1-1-111
χ51111-1-111-1-1-111111-1-1-1111ii−i−i111-11-1-1111ii−i−i-1ii−i−iii−i−i-111-1-11-1-1111-1ii−i−i-1i−i
χ61111-1-111-1-1-111111-1-1-1111−i−iii111-11-1-1111−i−iii-1−i−iii−i−iii-111-1-11-1-1111-1−i−iii-1−ii
χ71111-1-111-1-1-11-1-11111-11-11ii−i−i-1-111-111111−i−iii-1ii−i−i−i−iii-1-1-1111-1-1-1-11-1ii−i−i1−ii
χ81111-1-111-1-1-11-1-11111-11-11−i−iii-1-111-111111ii−i−i-1−i−iiiii−i−i-1-1-1111-1-1-1-11-1−i−iii1i−i
χ9222222222222002200220222220020000-1-12000022222000020000-1-1-100-1-1-1-1-1-1000
χ102222222222220022002202-2-2-2-20020000-1-1200002-2-2-2-2000020000-1-1-100-1-11111000
χ112222-2-222-2-2-22002200-22022i2i−2i−2i0020000-1-120000-22i2i−2i−2i0000-20000-11100-11−i−iii000
χ122222-2-222-2-2-22002200-2202−2i−2i2i2i0020000-1-120000-2−2i−2i2i2i0000-20000-11100-11ii−i−i000
χ133333333333331133113-11-1333311-1111100-11111-1-1-1-1-11111-11111000-1-1000000-1-1-1
χ143333333333331133113-11-1-3-3-3-311-1111100-1-1-1-1-1-11111-1-1-1-1-11111000-1-1000000-111
χ15333333333333-1-133-1-13-1-1-13333-1-1-1-1-1-1-100-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100011000000111
χ16333333333333-1-133-1-13-1-1-1-3-3-3-3-1-1-1-1-1-1-100-11111-111111111-1-1-1-1-1000110000001-1-1
χ173333-3-333-3-3-331133-1-1-3-11-13i3i−3i−3i11-1-11-1-100-1ii−i−i1−i−iiiii−i−i111-1-1000-1-10000001−ii
χ183333-3-333-3-3-331133-1-1-3-11-1−3i−3i3i3i11-1-11-1-100-1−i−iii1ii−i−i−i−iii111-1-1000-1-10000001i−i
χ193333-3-333-3-3-33-1-13311-3-1-1-13i3i−3i−3i-1-1-11-11100-1−i−iii1−i−iii−i−iii1-1-11100011000000-1i−i
χ203333-3-333-3-3-33-1-13311-3-1-1-1−3i−3i3i3i-1-1-11-11100-1ii−i−i1ii−i−iii−i−i1-1-11100011000000-1−ii
χ21444-444-44-400022002200202-22-22-20-2-22-21100000000002-22-20000011100-1-11-11-1000
χ22444-444-44-40002200220020-22-222-20-2-22-2110000000000-22-220000011100-1-1-11-11000
χ23444-444-44-4000-2-200-2-200-202-22-2-22022-22110000000000-22-220000011100-1-11-11-1000
χ24444-444-44-4000-2-200-2-200-20-22-22-22022-221100000000002-22-20000011100-1-1-11-11000
χ25444-4-4-4-4440002200-2-200202i−2i−2i2i2-202-2-221100000000002i−2i−2i2i000001-1-100-11i−i−ii000
χ26444-4-4-4-4440002200-2-20020−2i2i2i−2i2-202-2-22110000000000−2i2i2i−2i000001-1-100-11−iii−i000
χ27444-4-4-4-444000-2-2002200-202i−2i−2i2i-220-222-2110000000000−2i2i2i−2i000001-1-100-11i−i−ii000
χ28444-4-4-4-444000-2-2002200-20−2i2i2i−2i-220-222-21100000000002i−2i−2i2i000001-1-100-11−iii−i000
χ29666666666-2-2-200-2-200-2-20-2000000-200000022222-20000-2-2-2-22000000000000000000
χ30666666666-2-2-200-2-200-2-20-2000000-20000002-2-2-2-2-2000022222000000000000000000
χ31666666666-2-2-222-2-222-22220000222222200-20000200000000-2-2-2-2-200000000000000
χ32666666666-2-2-2-2-2-2-2-2-2-22-220000-2-22-2-2-2-200-20000200000000-2222200000000000000
χ336666-6-666-622-200-2-2002-20-2000000-200000022i2i−2i−2i20000−2i−2i2i2i-2000000000000000000
χ346666-6-666-622-200-2-2002-20-2000000-20000002−2i−2i2i2i200002i2i−2i−2i-2000000000000000000
χ356666-6-666-622-222-2-2-2-222220000222-22-2-200-20000-2000000002-2-22200000000000000
χ366666-6-666-622-2-2-2-2-22222-220000-2-222-22200-20000-200000000222-2-200000000000000
χ37888-888-88-800000000000004-44-40000000-1-10000000000000000000-1-1-10011-11-11000
χ38888-888-88-80000000000000-44-440000000-1-10000000000000000000-1-1-100111-11-1000
χ39888-8-8-8-88800000000000004i−4i−4i4i0000000-1-10000000000000000000-111001-1−iii−i000
χ40888-8-8-8-8880000000000000−4i4i4i−4i0000000-1-10000000000000000000-111001-1i−i−ii000
χ4188-804-40004-4-444404-400-4000000000000220000000000000002-22-2-22-200000000000
χ4288-804-40004-4-4-4-440-4400400000000000022000000000000000-22-22-22-200000000000
χ4388-80-44000-44-44440-4400-4000000000000220000000000000002-2-22-2-2200000000000
χ4488-80-44000-44-4-4-4404-400400000000000022000000000000000-222-2-2-2200000000000
χ451212121200-4-40004004-4440-40-4000000440-4-400000000000000000000000000000000000
χ461212121200-4-40004004-4-4-40-40-40000004-404400000000000000000000000000000000000
χ471212121200-4-40004444-40004440000-4-4-4040000000000000000000000000000000000000
χ481212121200-4-40004-4-44-40004-44000044-40-40000000000000000000000000000000000000
χ49121212-12004-40440220022-40200000-220-2-2-220002-22-202-22-200000000000000000000000
χ50121212-12004-40440220022-40200000-220-2-2-22000-22-220-22-2200000000000000000000000
χ51121212-12004-40440-2-200-2-2-40-2000002-20222-20002-22-20-22-2200000000000000000000000
χ52121212-12004-40440-2-200-2-2-40-2000002-20222-2000-22-2202-22-200000000000000000000000
χ53121212-12004-40-4-402200-2-240200000-2202-22-20002i−2i−2i2i02i−2i−2i2i00000000000000000000000
χ54121212-12004-40-4-402200-2-240200000-2202-22-2000−2i2i2i−2i0−2i2i2i−2i00000000000000000000000
χ55121212-12004-40-4-40-2-2002240-2000002-20-22-220002i−2i−2i2i0−2i2i2i−2i00000000000000000000000
χ56121212-12004-40-4-40-2-2002240-2000002-20-22-22000−2i2i2i−2i02i−2i−2i2i00000000000000000000000
χ571616-1608-80008-8-8008000000000000000000-2-200000000000000000002-2200000000000
χ581616-160-88000-88-8008000000000000000000-2-2000000000000000000022-200000000000
χ5916-1600000000008-800000-404000000000004-400000000000000000000002-2000000000
χ6016-160000000000-8800000-404000000000004-40000000000000000000000-22000000000
χ612424242400-8-8000-800-880000000000000000000000000000000000000000000000000000
χ622424-24012-12000-44444-404-400-400000000000000000000000000000-22-2200000000000000
χ632424-24012-12000-444-4-4-40-44004000000000000000000000000000002-22-200000000000000
χ642424-240-12120004-4444-40-4400-400000000000000000000000000000-222-200000000000000
χ652424-240-12120004-44-4-4-404-4004000000000000000000000000000002-2-2200000000000000
χ6632-3200000000000000000-80800000000000-44000000000000000000000000000000000
χ6748-4800000000008-80000040-400000000000000000000000000000000000-22000000000
χ6848-480000000000-880000040-4000000000000000000000000000000000002-2000000000

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