Finite Group Databasebeta

← Group #72261592

Character table — Group #72261592

Order 6144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82
size1133333344661212121212121212121212121212242424242424242424242424242448484848484848484848969696969696969696969696969696969696969696969696192192192192512512512512
order1222222222222222224444444422444444444444444444444444444444888888888888888888883666
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111-1-111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11111111111-1-1-1-11-11-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111-1-111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11111111111-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ5222222222222222222222222222222222222222222222222220000000000000000000000000000-1-1-1-1
χ622222222-2-222-2-2-2-2-2-222-2-2-2-222-2-222-2-2-2-2-2-22222222222-2-2-2-20000000000000000000000000000-1-111
χ72-2222-2-2-22-22-2222-2-2-2220000-2-22-22-200000000000000000000000000002222−2−2−2−22222−2−2−2−20000-111-1
χ82-2222-2-2-22-22-2222-2-2-2220000-2-22-22-20000000000000000000000000000−2−2−2−22222−2−2−2−222220000-111-1
χ92-2222-2-2-2-222-2-2-2-2222220000-2-2-222-200000000000000000000000000002222−2−2−2−2−2−2−2−222220000-11-11
χ102-2222-2-2-2-222-2-2-2-2222220000-2-2-222-20000000000000000000000000000−2−2−2−222222222−2−2−2−20000-11-11
χ1133333333333333333333-1-1-1-1333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111110000
χ1233333333333333333333-1-1-1-1333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-10000
χ133333333333333-1-13-1-1-1-13333-1-1-1-1-1-133-1-1-1-133-1-13-1-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-111-1-1-1-1-1-10000
χ143333333333333-1-13-1-1-1-13333-1-1-1-1-1-133-1-1-1-133-1-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111110000
χ153333333333333-1-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333-1-133-13-1-1-1-1-1-1-1-111111111-1-111-1-111-1-111-1-111-1-1-1-10000
χ163333333333333-1-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333-1-133-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111110000
χ1733333333-3-333-311-311-1-11111-1-111-1-111-3-3-3-3-1-133-13-1-1-1-111111-11-111-1-1-1-111-1-11111-1-111-1-1-1-1110000
χ1833333333-3-333-311-311-1-11111-1-111-1-111-3-3-3-3-1-133-13-1-1-1-11111-11-11-1-11111-1-111-1-1-1-111-1-11111-1-10000
χ1933333333-3-333-311-311-1-1-3-3-3-3-1-111-1-1-3-3111133-1-13-1-1-1-1-111111-11-111-1-111-1-111-1-1-1-111-1-111-1-1110000
χ2033333333-3-333-311-311-1-1-3-3-3-3-1-111-1-1-3-3111133-1-13-1-1-1-1-11111-11-11-1-111-1-111-1-11111-1-111-1-111-1-10000
χ2133333333-3-333-3-3-3-3-3-333111133-3-333111111-1-1-1-1-1-1-1-1-1-111111-11-111-1-1-1-1-1-1-1-1-1-11111111111-1-10000
χ2233333333-3-333-3-3-3-3-3-333111133-3-333111111-1-1-1-1-1-1-1-1-1-11111-11-11-1-11111111111-1-1-1-1-1-1-1-1-1-1110000
χ2333-1-133-1-133-1-1-13-1-13-13-1−1+2i−1+2i−1−2i−1−2i3-1-1-1-1-11111−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i1111−1+2i−1−2i11−1+2i−1−2i1111-1-1-1-1i−ii−ii−ii−ii−ii−ii−ii−i1-11-10000
χ2433-1-133-1-133-1-1-13-1-13-13-1−1+2i−1+2i−1−2i−1−2i3-1-1-1-1-11111−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i1111−1+2i−1−2i11−1+2i−1−2i-1-1-1-11111−ii−ii−ii−ii−ii−ii−ii−ii-11-110000
χ2533-1-133-1-133-1-1-13-1-13-13-1−1−2i−1−2i−1+2i−1+2i3-1-1-1-1-11111−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i1111−1−2i−1+2i11−1−2i−1+2i1111-1-1-1-1−ii−ii−ii−ii−ii−ii−ii−ii1-11-10000
χ2633-1-133-1-133-1-1-13-1-13-13-1−1−2i−1−2i−1+2i−1+2i3-1-1-1-1-11111−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i1111−1−2i−1+2i11−1−2i−1+2i-1-1-1-11111i−ii−ii−ii−ii−ii−ii−ii−i-11-110000
χ2733-1-133-1-133-1-1-1-13-1-13-13−1+2i−1+2i−1−2i−1−2i-13-1-1-1-11111−1−2i−1+2i−1+2i−1−2i−1−2i−1+2i11−1+2i−1−2i11−1+2i−1−2i111111-1-1-1-1i−i−iii−i−iii−i−iii−i−ii-11-110000
χ2833-1-133-1-133-1-1-1-13-1-13-13−1+2i−1+2i−1−2i−1−2i-13-1-1-1-11111−1−2i−1+2i−1+2i−1−2i−1−2i−1+2i11−1+2i−1−2i11−1+2i−1−2i11-1-1-1-11111−iii−i−iii−i−iii−i−iii−i1-11-10000
χ2933-1-133-1-133-1-1-1-13-1-13-13−1−2i−1−2i−1+2i−1+2i-13-1-1-1-11111−1+2i−1−2i−1−2i−1+2i−1+2i−1−2i11−1−2i−1+2i11−1−2i−1+2i111111-1-1-1-1−iii−i−iii−i−iii−i−iii−i-11-110000
χ3033-1-133-1-133-1-1-1-13-1-13-13−1−2i−1−2i−1+2i−1+2i-13-1-1-1-11111−1+2i−1−2i−1−2i−1+2i−1+2i−1−2i11−1−2i−1+2i11−1−2i−1+2i11-1-1-1-11111i−i−iii−i−iii−i−iii−i−ii1-11-10000
χ3133-1-133-1-1-3-3-1-111-311-3-131+2i1+2i1−2i1−2i-1311-1-1-1-1-1-11−2i1+2i−1−2i−1+2i−1+2i−1−2i11−1−2i−1+2i111+2i1−2i-1-11-11-1-1-111−iii−i−iii−ii−i−iii−i−ii-111-10000
χ3233-1-133-1-1-3-3-1-111-311-3-131+2i1+2i1−2i1−2i-1311-1-1-1-1-1-11−2i1+2i−1−2i−1+2i−1+2i−1−2i11−1−2i−1+2i111+2i1−2i-1-1-11-1111-1-1i−i−iii−i−ii−iii−i−iii−i1-1-110000
χ3333-1-133-1-1-3-3-1-111-311-3-131−2i1−2i1+2i1+2i-1311-1-1-1-1-1-11+2i1−2i−1+2i−1−2i−1−2i−1+2i11−1+2i−1−2i111−2i1+2i-1-11-11-1-1-111i−i−iii−i−ii−iii−i−iii−i-111-10000
χ3433-1-133-1-1-3-3-1-111-311-3-131−2i1−2i1+2i1+2i-1311-1-1-1-1-1-11+2i1−2i−1+2i−1−2i−1−2i−1+2i11−1+2i−1−2i111−2i1+2i-1-1-11-1111-1-1−iii−i−iii−ii−i−iii−i−ii1-1-110000
χ3533-1-133-1-1-3-3-1-11-311-313-11+2i1+2i1−2i1−2i3-111-1-1-1-1-1-11+2i1−2i−1−2i−1+2i−1−2i−1+2i1111−1−2i−1+2i-1-11+2i1−2i1-11-1-1-111−ii−ii−ii−iii−ii−ii−ii−i1-1-110000
χ3633-1-133-1-1-3-3-1-11-311-313-11+2i1+2i1−2i1−2i3-111-1-1-1-1-1-11+2i1−2i−1−2i−1+2i−1−2i−1+2i1111−1−2i−1+2i-1-11+2i1−2i-11-1111-1-1i−ii−ii−ii−i−ii−ii−ii−ii-111-10000
χ3733-1-133-1-1-3-3-1-11-311-313-11−2i1−2i1+2i1+2i3-111-1-1-1-1-1-11−2i1+2i−1+2i−1−2i−1+2i−1−2i1111−1+2i−1−2i-1-11−2i1+2i1-11-1-1-111i−ii−ii−ii−i−ii−ii−ii−ii1-1-110000
χ3833-1-133-1-1-3-3-1-11-311-313-11−2i1−2i1+2i1+2i3-111-1-1-1-1-1-11−2i1+2i−1+2i−1−2i−1+2i−1−2i1111−1+2i−1−2i-1-11−2i1+2i-11-1111-1-1−ii−ii−ii−iii−ii−ii−ii−i-111-10000
χ394-4444-4-4-44-44-4444-4-4-4440000-4-44-44-40000000000000000000000000000000000000000000000001-1-11
χ404-4444-4-4-4-444-4-4-4-4444440000-4-4-444-40000000000000000000000000000000000000000000000001-11-1
χ416666666666666-2-26-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ4266666666-6-666-622-622-2-22222-2-222-2-2222222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ4366-2-266-2-266-2-2-26-2-26-26-222226-2-2-2-2-2-2-2-2-2222222-2-2-2-222-2-22200000000000000000000000000000000
χ4466-2-266-2-266-2-2-2-26-2-26-262222-26-2-2-2-2-2-2-2-2222222-2-222-2-222-2-200000000000000000000000000000000
χ4566-2-266-2-266-2-2-2-2-2-2-2-2-2-22222-2-22222-2-222−2+4i−2−4i22−2+4i−2−4i-222i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ4666-2-266-2-266-2-2-2-2-2-2-2-2-2-22222-2-22222-2-222−2−4i−2+4i22−2−4i−2+4i-22−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ4766-2-266-2-266-2-2-2-2-2-2-2-2-2-2−2+4i−2+4i−2−4i−2−4i-2-2222222-2-222−2+4i−2−4i222-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ4866-2-266-2-266-2-2-2-2-2-2-2-2-2-2−2−4i−2−4i−2+4i−2+4i-2-2222222-2-222−2−4i−2+4i222-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ4966-2-266-2-2-6-6-2-2222222-2-2-2-2-2-2-2-2-2-22222-2-22+4i2−4i22−2−4i−2+4i-22−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ5066-2-266-2-2-6-6-2-2222222-2-2-2-2-2-2-2-2-2-22222-2-22−4i2+4i22−2+4i−2−4i-222i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ5166-2-266-2-2-6-6-2-2222222-2-22+4i2+4i2−4i2−4i-2-2-2-222-2-222-2-2−2−4i−2+4i222-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ5266-2-266-2-2-6-6-2-2222222-2-22−4i2−4i2+4i2+4i-2-2-2-222-2-222-2-2−2+4i−2−4i222-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ5366-2-266-2-2-6-6-2-222-622-6-26-2-2-2-2-2622-2-22222-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ5466-2-266-2-2-6-6-2-22-622-626-2-2-2-2-26-222-2-22222-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ556-6666-6-6-66-66-66-2-2-622-2-2000022-22-22000000000000000000000000000022−2−2−2−22222−2−2−2−22200000000
χ566-6666-6-6-66-66-66-2-2-622-2-2000022-22-220000000000000000000000000000−2−22222−2−2−2−22222−2−200000000
χ576-6666-6-6-6-666-6-6226-2-2-2-20000222-2-22000000000000000000000000000022−2−2−2−222−2−22222−2−200000000
χ586-6666-6-6-6-666-6-6226-2-2-2-20000222-2-220000000000000000000000000000−2−22222−2−222−2−2−2−22200000000
χ596-6-2-26-6226-6-22-26-22-626-20000-62-22-220000000000000000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ606-6-2-26-6226-6-22-26-22-626-20000-62-22-220000000000000000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ616-6-2-26-6226-6-22-2-2622-6-2600002-6-22-220000000000000000000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000
χ626-6-2-26-6226-6-22-2-2622-6-2600002-6-22-220000000000000000000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000
χ636-6-2-26-622-66-2222-6-2-26-2600002-62-2-220000000000000000000000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000
χ646-6-2-26-622-66-2222-6-2-26-2600002-62-2-220000000000000000000000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000
χ656-6-2-26-622-66-222-62-26-26-20000-622-2-220000000000000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ666-6-2-26-622-66-222-62-26-26-20000-622-2-220000000000000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ67121212-4-4-412-400-4-4000000004-44-40000004-400000000000000000022-2-22-22-2000000000000000000000000
χ68121212-4-4-412-400-4-4000000004-44-40000004-4000000000000000000-2-222-22-22000000000000000000000000
χ69121212-4-4-412-400-4-400000000-44-44000000-440000000000000000002-2-222-2-22000000000000000000000000
χ70121212-4-4-412-400-4-400000000-44-44000000-44000000000000000000-222-2-222-2000000000000000000000000
χ711212-412-4-4-41200-4-4000000004-44-4000000-440000000000000000002-2-22-222-2000000000000000000000000
χ721212-412-4-4-41200-4-4000000004-44-4000000-44000000000000000000-222-22-2-22000000000000000000000000
χ731212-412-4-4-41200-4-400000000-44-440000004-400000000000000000022-2-2-22-22000000000000000000000000
χ741212-412-4-4-41200-4-400000000-44-440000004-4000000000000000000-2-2222-22-2000000000000000000000000
χ7512-12-4-412-124412-12-44-4-4-4444-4-40000444-44-40000000000000000000000000000000000000000000000000000
χ7612-12-4-412-1244-1212-44444-4-4-4-4-4000044-444-40000000000000000000000000000000000000000000000000000
χ772424-8-8-8-8-8-80088000000008i−8i−8i8i0000000000000000000000000000000000000000000000000000000000
χ782424-8-8-8-8-8-8008800000000−8i8i8i−8i0000000000000000000000000000000000000000000000000000000000
χ7924-2424-8-88-24800-880000000000000000000000000000000000000000000000000000000000000000000000
χ8024-24-824-888-2400-880000000000000000000000000000000000000000000000000000000000000000000000
χ8124-24-8-8-8888008-8000000000000000000008-8000000000000000000000000000000000000000000000000
χ8224-24-8-8-8888008-800000000000000000000-88000000000000000000000000000000000000000000000000

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