Finite Group Databasebeta

← Group #72226090

Character table — Group #72226090

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size112223333334466666666666661212121212121212121212123232323248484848484848484848484848484848646464646464
order12244224444882444444444444448888888888361212222444448888888861224242424
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ311111111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-11111-1-111-1-1-1-1
χ411111111111-1-1111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1111-1-1-1-11111-1-1-1-1
χ511-1-111111111-1-1-11111-1-111-1-11-1-11-11111-1-1-1-111111-11-1-11-11-1-111-1-111-1-111-1-1
χ611-1-111111111-1-1-11111-1-111-1-11-1-11-11111-1-1-1-11111-11-111-11-111-1-111-1-1-1-111-1-1
χ711-1-11111111-11-1-11111-1-111-1-11-1-1-11-1-1-1-1111111111-1-1111-1-11111-1-1-1-1-1-1-1-111
χ811-1-11111111-11-1-11111-1-111-1-11-1-1-11-1-1-1-111111111-111-1-1-111-1-1-1-11111-1-1-1-111
χ922222222222222222222222222222222222222-1-1-1-10000000000000000-1-1-1-1-1-1
χ1022222222222-2-2222222222222222-2-2-2-2-2-2-2-2-2-2-1-1-1-10000000000000000-1-11111
χ11222-2-2222222002-2-2-2-2-2-2-22222-2-22000000000022-2-200000000000000002-20000
χ12222-2-2222222002-2-2-2-2-2-2-22222-2-220000000000-1-1110000000000000000-113−33−3
χ13222-2-2222222002-2-2-2-2-2-2-22222-2-220000000000-1-1110000000000000000-11−33−33
χ1422-22-222222200-22-2-2-2-22222-2-2-22-2000000000022-2-20000000000000000-220000
χ1522-22-222222200-22-2-2-2-22222-2-2-22-20000000000-1-11100000000000000001-13−3−33
χ1622-22-222222200-22-2-2-2-22222-2-2-22-20000000000-1-11100000000000000001-1−333−3
χ1722-2-222222222-2-2-22222-2-222-2-22-2-22-22222-2-2-2-2-1-1-1-1000000000000000011-1-111
χ1822-2-22222222-22-2-22222-2-222-2-22-2-2-22-2-2-2-22222-1-1-1-100000000000000001111-1-1
χ193333333-1-1-1-13333-1-1-1-1-1-1-1-1-1-13-1-133-1-1-1-1-1-1-1-1000011111111-1-1-1-1-1-1-1-1000000
χ203333333-1-1-1-13333-1-1-1-1-1-1-1-1-1-13-1-133-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-111111111000000
χ213333333-1-1-1-1-3-333-1-1-1-1-1-1-1-1-1-13-1-1-3-311111111000011-1-1-111-111-1-1-1-111000000
χ223333333-1-1-1-1-3-333-1-1-1-1-1-1-1-1-1-13-1-1-3-3111111110000-1-1111-1-11-1-11111-1-1000000
χ2333333-1-1−1+2i−1−2i−1+2i−1−2i33-1-111−1+2i−1−2i−1+2i−1−2i11−1+2i−1−2i-111-1-111−1+2i−1−2i11−1+2i−1−2i00001111-1-1-1-1i−ii−ii−ii−i000000
χ2433333-1-1−1+2i−1−2i−1+2i−1−2i33-1-111−1+2i−1−2i−1+2i−1−2i11−1+2i−1−2i-111-1-111−1+2i−1−2i11−1+2i−1−2i0000-1-1-1-11111−ii−ii−ii−ii000000
χ2533333-1-1−1+2i−1−2i−1+2i−1−2i-3-3-1-111−1+2i−1−2i−1+2i−1−2i11−1+2i−1−2i-11111-1-11−2i1+2i-1-11−2i1+2i000011-1-11-1-11−iii−ii−i−ii000000
χ2633333-1-1−1+2i−1−2i−1+2i−1−2i-3-3-1-111−1+2i−1−2i−1+2i−1−2i11−1+2i−1−2i-11111-1-11−2i1+2i-1-11−2i1+2i0000-1-111-111-1i−i−ii−iii−i000000
χ2733333-1-1−1−2i−1+2i−1−2i−1+2i33-1-111−1−2i−1+2i−1−2i−1+2i11−1−2i−1+2i-111-1-111−1−2i−1+2i11−1−2i−1+2i00001111-1-1-1-1−ii−ii−ii−ii000000
χ2833333-1-1−1−2i−1+2i−1−2i−1+2i33-1-111−1−2i−1+2i−1−2i−1+2i11−1−2i−1+2i-111-1-111−1−2i−1+2i11−1−2i−1+2i0000-1-1-1-11111i−ii−ii−ii−i000000
χ2933333-1-1−1−2i−1+2i−1−2i−1+2i-3-3-1-111−1−2i−1+2i−1−2i−1+2i11−1−2i−1+2i-11111-1-11+2i1−2i-1-11+2i1−2i000011-1-11-1-11i−i−ii−iii−i000000
χ3033333-1-1−1−2i−1+2i−1−2i−1+2i-3-3-1-111−1−2i−1+2i−1−2i−1+2i11−1−2i−1+2i-11111-1-11+2i1−2i-1-11+2i1−2i0000-1-111-111-1−iii−ii−i−ii000000
χ3133-3-3333-1-1-1-13-3-3-3-1-1-1-111-1-1113113-3-1-1-1-1111100001-11-1-11-1111-1-111-1-1000000
χ3233-3-3333-1-1-1-13-3-3-3-1-1-1-111-1-1113113-3-1-1-1-111110000-11-111-11-1-1-111-1-111000000
χ3333-3-3333-1-1-1-1-33-3-3-1-1-1-111-1-111311-331111-1-1-1-100001-1-1111-1-1-1-1-1-11111000000
χ3433-3-3333-1-1-1-1-33-3-3-1-1-1-111-1-111311-331111-1-1-1-10000-111-1-1-1111111-1-1-1-1000000
χ3533-3-33-1-1−1+2i−1−2i−1+2i−1−2i3-31111−1+2i−1−2i1−2i1+2i111−2i1+2i-1-1-1-1111−1+2i−1−2i-1-11−2i1+2i00001-11-11-11-1−iii−i−iii−i000000
χ3633-3-33-1-1−1+2i−1−2i−1+2i−1−2i3-31111−1+2i−1−2i1−2i1+2i111−2i1+2i-1-1-1-1111−1+2i−1−2i-1-11−2i1+2i0000-11-11-11-11i−i−iii−i−ii000000
χ3733-3-33-1-1−1+2i−1−2i−1+2i−1−2i-331111−1+2i−1−2i1−2i1+2i111−2i1+2i-1-1-11-1-1-11−2i1+2i11−1+2i−1−2i00001-1-11-1-111i−ii−i−ii−ii000000
χ3833-3-33-1-1−1+2i−1−2i−1+2i−1−2i-331111−1+2i−1−2i1−2i1+2i111−2i1+2i-1-1-11-1-1-11−2i1+2i11−1+2i−1−2i0000-111-111-1-1−ii−iii−ii−i000000
χ3933-3-33-1-1−1−2i−1+2i−1−2i−1+2i3-31111−1−2i−1+2i1+2i1−2i111+2i1−2i-1-1-1-1111−1−2i−1+2i-1-11+2i1−2i00001-11-11-11-1i−i−iii−i−ii000000
χ4033-3-33-1-1−1−2i−1+2i−1−2i−1+2i3-31111−1−2i−1+2i1+2i1−2i111+2i1−2i-1-1-1-1111−1−2i−1+2i-1-11+2i1−2i0000-11-11-11-11−iii−i−iii−i000000
χ4133-3-33-1-1−1−2i−1+2i−1−2i−1+2i-331111−1−2i−1+2i1+2i1−2i111+2i1−2i-1-1-11-1-1-11+2i1−2i11−1−2i−1+2i00001-1-11-1-111−ii−iii−ii−i000000
χ4233-3-33-1-1−1−2i−1+2i−1−2i−1+2i-331111−1−2i−1+2i1+2i1−2i111+2i1−2i-1-1-11-1-1-11+2i1−2i11−1−2i−1+2i0000-111-111-1-1i−ii−i−ii−ii000000
χ434-4000-44-4-44400000000004-40000000000000004-4000000000000000000000000
χ444-4000-44-4-44400000000004-4000000000000000-2223−230000000000000000000000
χ454-4000-44-4-44400000000004-4000000000000000-22−23230000000000000000000000
χ4666666-2-2222266-2-2-2-22222-2-222-2-2-2-2-2-2-222-2-22200000000000000000000000000
χ4766666-2-22222-6-6-2-2-2-22222-2-222-2-2-22222-2-222-2-200000000000000000000000000
χ48666-6-666-2-2-2-2006-6222222-2-2-2-2-62-2000000000000000000000000000000000000
χ49666-6-6-2-2222200-2222-2-2-2-2-2-22222-2004-4004-40000000000000000000000000000
χ50666-6-6-2-2222200-2222-2-2-2-2-2-22222-200-4400-440000000000000000000000000000
χ51666-6-6-2-2−2+4i−2−4i−2+4i−2−4i00-22-2-22−4i2+4i2−4i2+4i22−2+4i−2−4i2-22000000000000000000000000000000000000
χ52666-6-6-2-2−2−4i−2+4i−2−4i−2+4i00-22-2-22+4i2−4i2+4i2−4i22−2−4i−2+4i2-22000000000000000000000000000000000000
χ5366-66-666-2-2-2-200-662222-2-2-2-222-6-22000000000000000000000000000000000000
χ5466-66-6-2-22222002-222-2-222-2-2-2-22-22004-400-440000000000000000000000000000
χ5566-66-6-2-22222002-222-2-222-2-2-2-22-2200-44004-40000000000000000000000000000
χ5666-66-6-2-2−2+4i−2−4i−2+4i−2−4i002-2-2-22−4i2+4i−2+4i−2−4i222−4i2+4i22-2000000000000000000000000000000000000
χ5766-66-6-2-2−2−4i−2+4i−2−4i−2+4i002-2-2-22+4i2−4i−2−4i−2+4i222+4i2−4i22-2000000000000000000000000000000000000
χ5866-6-66-2-222226-622-2-222-2-2-2-2-2-2-222-22-2-22222-2-200000000000000000000000000
χ5966-6-66-2-22222-6622-2-222-2-2-2-2-2-2-2222-222-2-2-2-22200000000000000000000000000
χ6012-120004-4-4-44400008-80000-4400000000000000000000000000000000000000000
χ6112-120004-4-4-4440000-880000-4400000000000000000000000000000000000000000
χ6212-120004-44+8i4−8i−4−8i−4+8i00000000004-400000000000000000000000000000000000000000
χ6312-120004-44−8i4+8i−4+8i−4−8i00000000004-400000000000000000000000000000000000000000
χ6412-12000-121244-4-40000000000-4400000000000000000000000000000000000000000

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