Finite Group Databasebeta

← Group #72240363

Character table — Group #72240363

Order 6144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88
size11333333446612121212121212121212121212121212121224242424242424242424242448484848484848484848484848484848484848484848484848489696969696969696192192192192192192192192512512512512
order1222222222222222224444444444442244444444444444444444888888888888888888888888444444443666
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−ii−iiii−i−i−i11-1-1
χ411111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−ii−i−i−iiii11-1-1
χ5222222222222222222222222222222222222222222222222222200000000000000000000000000000000-1-1-1-1
χ622222222-2-222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2222222-2-2-2-200000000000000000000000000000000-1-111
χ72-222-22-2-22-22-2222-2-2-222-2-2000000002-22-20000000000000000002222−2−2−2−22222−2−2−2−222−2−222−2−200000000-111-1
χ82-222-22-2-22-22-2222-2-2-222-2-2000000002-22-2000000000000000000−2−2−2−22222−2−2−2−22222−2−222−2−22200000000-111-1
χ92-222-22-2-2-222-2-2-2-222222-2-200000000-222-2000000000000000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2i2i2−i2−i2−i2−i2i2i200000000-11-11
χ102-222-22-2-2-222-2-2-2-222222-2-200000000-222-2000000000000000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000-11-11
χ113333333333333333333333-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-10000
χ123333333333333333333333-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111110000
χ133333333333333-1-13-1-1-1-1-1-133-1-1-1-133-1-1-1-133-1-133-1-13-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111-1-11-1-10000
χ143333333333333-1-13-1-1-1-1-1-133-1-1-1-133-1-1-1-133-1-133-1-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1110000
χ153333333333333-1-13-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-133-1-133-13-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-111-1110000
χ163333333333333-1-13-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-133-1-133-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-10000
χ1733333333-3-333-311-311-1-1-1-111-3-3-3-31111-1-1-1-13311-3-3-13-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii−ii−iiii−i−i0000
χ1833333333-3-333-311-311-1-1-1-111-3-3-3-31111-1-1-1-13311-3-3-13-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−ii−ii−i−i−iii0000
χ1933333333-3-333-311-311-1-1-1-1-3-31111-3-311-1-133-1-1-3-3113-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiii−ii−i−i−iii0000
χ2033333333-3-333-311-311-1-1-1-1-3-31111-3-311-1-133-1-1-3-3113-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−ii−iiii−i−i0000
χ2133333333-3-333-3-3-3-3-3-3333311111111-3-333-1-1-1-11111-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i−ii−i−i−iiii0000
χ2233333333-3-333-3-3-3-3-3-3333311111111-3-333-1-1-1-11111-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiiii−iiii−i−i−i0000
χ2333-1-133-1-133-1-1-13-1-13-13-13-1−1+2i−1−2i−1+2i−1+2i−1−2i−1−2i−1+2i−1−2i-1-1-1-1−1+2i−1−2i−1+2i−1−2i11111111−1+2i−1−2i11−1+2i−1−2iii−i−iii−i−iii−i−iii−i−ii−ii−ii−ii−i-1-111-111-10000
χ2433-1-133-1-133-1-1-13-1-13-13-13-1−1+2i−1−2i−1+2i−1+2i−1−2i−1−2i−1+2i−1−2i-1-1-1-1−1+2i−1−2i−1+2i−1−2i11111111−1+2i−1−2i11−1+2i−1−2i−i−iii−i−iii−i−iii−i−iii−ii−ii−ii−ii11-1-11-1-110000
χ2533-1-133-1-133-1-1-13-1-13-13-13-1−1−2i−1+2i−1−2i−1−2i−1+2i−1+2i−1−2i−1+2i-1-1-1-1−1−2i−1+2i−1−2i−1+2i11111111−1−2i−1+2i11−1−2i−1+2iii−i−iii−i−iii−i−iii−i−ii−ii−ii−ii−i11-1-11-1-110000
χ2633-1-133-1-133-1-1-13-1-13-13-13-1−1−2i−1+2i−1−2i−1−2i−1+2i−1+2i−1−2i−1+2i-1-1-1-1−1−2i−1+2i−1−2i−1+2i11111111−1−2i−1+2i11−1−2i−1+2i−i−iii−i−iii−i−iii−i−iii−ii−ii−ii−ii-1-111-111-10000
χ2733-1-133-1-133-1-1-1-13-1-13-13-13−1+2i−1−2i−1−2i−1−2i−1+2i−1+2i−1+2i−1−2i-1-1-1-1−1+2i−1−2i−1−2i−1+2i111111−1+2i−1−2i11−1+2i−1−2i11ii−i−iii−i−iii−i−iii−i−i−ii−ii−ii−ii-1-11-111-110000
χ2833-1-133-1-133-1-1-1-13-1-13-13-13−1+2i−1−2i−1−2i−1−2i−1+2i−1+2i−1+2i−1−2i-1-1-1-1−1+2i−1−2i−1−2i−1+2i111111−1+2i−1−2i11−1+2i−1−2i11−i−iii−i−iii−i−iii−i−iiii−ii−ii−ii−i11-11-1-11-10000
χ2933-1-133-1-133-1-1-1-13-1-13-13-13−1−2i−1+2i−1+2i−1+2i−1−2i−1−2i−1−2i−1+2i-1-1-1-1−1−2i−1+2i−1+2i−1−2i111111−1−2i−1+2i11−1−2i−1+2i11ii−i−iii−i−iii−i−iii−i−i−ii−ii−ii−ii11-11-1-11-10000
χ3033-1-133-1-133-1-1-1-13-1-13-13-13−1−2i−1+2i−1+2i−1+2i−1−2i−1−2i−1−2i−1+2i-1-1-1-1−1−2i−1+2i−1+2i−1−2i111111−1−2i−1+2i11−1−2i−1+2i11−i−iii−i−iii−i−iii−i−iiii−ii−ii−ii−i-1-11-111-110000
χ3133-1-133-1-1-3-3-1-111-311-3-13-131+2i1−2i1−2i1−2i1+2i1+2i1+2i1−2i11-1-1−1−2i−1+2i−1+2i−1−2i-1-1-1-111−1−2i−1+2i111+2i1−2i-1-111-1-111-1-1-1-111-1-111-11-111-11-1−iii−ii−ii−i0000
χ3233-1-133-1-1-3-3-1-111-311-3-13-131+2i1−2i1−2i1−2i1+2i1+2i1+2i1−2i11-1-1−1−2i−1+2i−1+2i−1−2i-1-1-1-111−1−2i−1+2i111+2i1−2i-1-1-1-111-1-11111-1-111-1-11-11-1-11-11i−i−ii−ii−ii0000
χ3333-1-133-1-1-3-3-1-111-311-3-13-131−2i1+2i1+2i1+2i1−2i1−2i1−2i1+2i11-1-1−1+2i−1−2i−1−2i−1+2i-1-1-1-111−1+2i−1−2i111−2i1+2i-1-111-1-111-1-1-1-111-1-111-11-111-11-1i−i−ii−ii−ii0000
χ3433-1-133-1-1-3-3-1-111-311-3-13-131−2i1+2i1+2i1+2i1−2i1−2i1−2i1+2i11-1-1−1+2i−1−2i−1−2i−1+2i-1-1-1-111−1+2i−1−2i111−2i1+2i-1-1-1-111-1-11111-1-111-1-11-11-1-11-11−iii−ii−ii−i0000
χ3533-1-133-1-1-3-3-1-11-311-313-13-11+2i1−2i1+2i1+2i1−2i1−2i1+2i1−2i11-1-1−1−2i−1+2i−1−2i−1+2i-1-1-1-11111−1−2i−1+2i-1-11+2i1−2i11-1-111-1-1-1-111-1-1111-11-1-11-11−iiii−i−i−ii0000
χ3633-1-133-1-1-3-3-1-11-311-313-13-11+2i1−2i1+2i1+2i1−2i1−2i1+2i1−2i11-1-1−1−2i−1+2i−1−2i−1+2i-1-1-1-11111−1−2i−1+2i-1-11+2i1−2i-1-111-1-11111-1-111-1-1-11-111-11-1i−i−i−iiii−i0000
χ3733-1-133-1-1-3-3-1-11-311-313-13-11−2i1+2i1−2i1−2i1+2i1+2i1−2i1+2i11-1-1−1+2i−1−2i−1+2i−1−2i-1-1-1-11111−1+2i−1−2i-1-11−2i1+2i11-1-111-1-1-1-111-1-1111-11-1-11-11i−i−i−iiii−i0000
χ3833-1-133-1-1-3-3-1-11-311-313-13-11−2i1+2i1−2i1−2i1+2i1+2i1−2i1+2i11-1-1−1+2i−1−2i−1+2i−1−2i-1-1-1-11111−1+2i−1−2i-1-11−2i1+2i-1-111-1-11111-1-111-1-1-11-111-11-1−iiii−i−i−ii0000
χ394-444-44-4-44-44-4444-4-4-444-4-4000000004-44-4000000000000000000000000000000000000000000000000001-1-11
χ404-444-44-4-4-444-4-4-4-444444-4-400000000-444-4000000000000000000000000000000000000000000000000001-11-1
χ416666666666666-2-26-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ4266666666-6-666-622-622-2-2-2-22222222222-2-2-2-2-2-22222-2-22222-2-2-2-2000000000000000000000000000000000000
χ4366-2-266-2-266-2-2-26-2-26-26-26-222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ4466-2-266-2-266-2-2-2-26-2-26-26-2622222222-2-2-2-22222-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ4566-2-266-2-266-2-2-2-2-2-2-2-2-2-2-2-222−2+4i−2+4i−2−4i−2−4i22222222−2+4i−2−4i-2-222-222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ4666-2-266-2-266-2-2-2-2-2-2-2-2-2-2-2-222−2−4i−2−4i−2+4i−2+4i22222222−2−4i−2+4i-2-222-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ4766-2-266-2-266-2-2-2-2-2-2-2-2-2-2-2-2−2+4i−2−4i2222−2+4i−2−4i2222−2+4i−2−4i2222-2-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ4866-2-266-2-266-2-2-2-2-2-2-2-2-2-2-2-2−2−4i−2+4i2222−2−4i−2+4i2222−2−4i−2+4i2222-2-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ4966-2-266-2-2-6-6-2-2222222-2-2-2-2-2-22+4i2+4i2−4i2−4i-2-2-2-22222−2−4i−2+4i22-2-2-22−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ5066-2-266-2-2-6-6-2-2222222-2-2-2-2-2-22−4i2−4i2+4i2+4i-2-2-2-22222−2+4i−2−4i22-2-2-222i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ5166-2-266-2-2-6-6-2-2222222-2-2-2-22+4i2−4i-2-2-2-22+4i2−4i-2-222−2−4i−2+4i22-2-2222-22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ5266-2-266-2-2-6-6-2-2222222-2-2-2-22−4i2+4i-2-2-2-22−4i2+4i-2-222−2+4i−2−4i22-2-2222-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ5366-2-266-2-2-6-6-2-222-622-6-26-26-2-2-2-2-2-2-2-222-2-222222222-2-222-2-2-2-222000000000000000000000000000000000000
χ5466-2-266-2-2-6-6-2-22-622-626-26-2-2-2-2-2-2-2-2-222-2-222222222-2-2-2-22222-2-2000000000000000000000000000000000000
χ556-666-66-6-66-66-66-2-2-622-2-22200000000-22-220000000000000000002222−2−2−2−22222−2−2−2−2−2−222−2−222000000000000
χ566-666-66-6-66-66-66-2-2-622-2-22200000000-22-22000000000000000000−2−2−2−22222−2−2−2−2222222−2−222−2−2000000000000
χ576-666-66-6-6-666-6-6226-2-2-2-222000000002-2-22000000000000000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ586-666-66-6-6-666-6-6226-2-2-2-222000000002-2-22000000000000000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ596-6-2-2-66226-6-22-26-22-626-2-6200000000-22-22000000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ606-6-2-2-66226-6-22-26-22-626-2-6200000000-22-22000000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ616-6-2-2-66226-6-22-2-2622-6-262-600000000-22-22000000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ626-6-2-2-66226-6-22-2-2622-6-262-600000000-22-22000000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ636-6-2-2-6622-66-2222-6-2-26-262-6000000002-2-2200000000000000000022−2−2−2−222−2−22222−2−2−222−22−2−22000000000000
χ646-6-2-2-6622-66-2222-6-2-26-262-6000000002-2-22000000000000000000−2−22222−2−222−2−2−2−2222−2−22−222−2000000000000
χ656-6-2-2-6622-66-222-62-26-26-2-62000000002-2-2200000000000000000022−2−2−2−222−2−22222−2−22−2−22−222−2000000000000
χ666-6-2-2-6622-66-222-62-26-26-2-62000000002-2-22000000000000000000−2−22222−2−222−2−2−2−222−222−22−2−22000000000000
χ67121212-4-4-412-400-4-40000000000440000-4-4000000004-40000000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00000000000000000000
χ68121212-4-4-412-400-4-40000000000440000-4-4000000004-4000000000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ69121212-4-4-412-400-4-40000000000-4-400004400000000-440000000000002-22-22-22-2-22-22-22-2200000000000000000000
χ70121212-4-4-412-400-4-40000000000-4-400004400000000-44000000000000-22-22-22-222-22-22-22-200000000000000000000
χ711212-412-4-4-41200-4-40000000000440000-4-400000000-440000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ721212-412-4-4-41200-4-40000000000440000-4-400000000-44000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i00000000000000000000
χ731212-412-4-4-41200-4-40000000000-4-4000044000000004-40000000000002-2-222-2-222-2-222-2-2200000000000000000000
χ741212-412-4-4-41200-4-40000000000-4-4000044000000004-4000000000000-222-2-222-2-222-2-222-200000000000000000000
χ7512-1212-44-4-12400-440000000000004i−4i4i−4i0000000000004i−4i00000000002ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ32ζ300000000000000000000
χ7612-1212-44-4-12400-440000000000004i−4i4i−4i0000000000004i−4i0000000000−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ300000000000000000000
χ7712-1212-44-4-12400-44000000000000−4i4i−4i4i000000000000−4i4i00000000002ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ00000000000000000000
χ7812-1212-44-4-12400-44000000000000−4i4i−4i4i000000000000−4i4i0000000000−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ−2ζ00000000000000000000
χ7912-12-4124-44-1200-440000000000004i−4i4i−4i000000000000−4i4i00000000002ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ32ζ300000000000000000000
χ8012-12-4124-44-1200-440000000000004i−4i4i−4i000000000000−4i4i0000000000−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ3−2ζ300000000000000000000
χ8112-12-4124-44-1200-44000000000000−4i4i−4i4i0000000000004i−4i00000000002ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ2ζ00000000000000000000
χ8212-12-4124-44-1200-44000000000000−4i4i−4i4i0000000000004i−4i0000000000−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ−2ζ00000000000000000000
χ8312-12-4-4-12124412-12-44-4-4-4444-4-444000000004-44-4000000000000000000000000000000000000000000000000000000
χ8412-12-4-4-121244-1212-44444-4-4-4-4-44400000000-444-4000000000000000000000000000000000000000000000000000000
χ852424-8-8-8-8-8-8008800000000008i−8i0000−8i8i0000000000000000000000000000000000000000000000000000000000
χ862424-8-8-8-8-8-800880000000000−8i8i00008i−8i0000000000000000000000000000000000000000000000000000000000
χ8724-24-8-88-888008-80000000000008-8-88000000000000000000000000000000000000000000000000000000000000
χ8824-24-8-88-888008-8000000000000-888-8000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.