Finite Group Databasebeta

← Group #13181813

Character table — Group #13181813

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size12368881818369182424245454481224323232727248122432323272721236888181836918242424545448122432323272724812243232327272
order1326333242626666243366333612336633361226266662426266662466666666126666666612
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111-1-11111111-1-11111111-1-11111111-1-11111111-1-11111111-1-11111111-1-11111111-1-1
χ32222-1-1-1002222-1-1-1002222-1-1-1002222-1-1-1002222-1-1-1002222-1-1-1002222-1-1-1002222-1-1-100
χ42-12-12-1-1002-12-12-1-1002-12-12-1-1002-12-12-1-1002-12-12-1-1002-12-12-1-1002-12-12-1-1002-12-12-1-100
χ52-12-1-12-1002-12-1-12-1002-12-1-12-1002-12-1-12-1002-12-1-12-1002-12-1-12-1002-12-1-12-1002-12-1-12-100
χ62-12-1-1-12002-12-1-1-12002-12-1-1-12002-12-1-1-12002-12-1-1-12002-12-1-1-12002-12-1-1-12002-12-1-1-1200
χ733-1-10001-133-1-10001-133-1-10001-133-1-10001-133-1-10001-133-1-10001-133-1-10001-133-1-10001-1
χ833-1-1000-1133-1-1000-1133-1-1000-1133-1-1000-1133-1-1000-1133-1-1000-1133-1-1000-1133-1-1000-11
χ96-3-21000006-3-21000006-3-21000006-3-21000006-3-21000006-3-21000006-3-21000006-3-2100000
χ10111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ111111111-1-11111111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321111111-1-11111111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ122222-1-1-1002222-1-1-100−1+i3−1+i3−1+i3−1+i31−i321−i321−i3200−1−i3−1−i3−1−i3−1−i31+i321+i321+i32002222-1-1-1002222-1-1-100−1+i3−1+i3−1+i3−1+i31−i321−i321−i3200−1−i3−1−i3−1−i3−1−i31+i321+i321+i3200
χ132-12-12-1-1002-12-12-1-100−1+i31−i32−1+i31−i32−1+i31−i321−i3200−1−i31+i32−1−i31+i32−1−i31+i321+i32002-12-12-1-1002-12-12-1-100−1+i31−i32−1+i31−i32−1+i31−i321−i3200−1−i31+i32−1−i31+i32−1−i31+i321+i3200
χ142-12-1-12-1002-12-1-12-100−1+i31−i32−1+i31−i321−i32−1+i31−i3200−1−i31+i32−1−i31+i321+i32−1−i31+i32002-12-1-12-1002-12-1-12-100−1+i31−i32−1+i31−i321−i32−1+i31−i3200−1−i31+i32−1−i31+i321+i32−1−i31+i3200
χ152-12-1-1-12002-12-1-1-1200−1+i31−i32−1+i31−i321−i321−i32−1+i300−1−i31+i32−1−i31+i321+i321+i32−1−i3002-12-1-1-12002-12-1-1-1200−1+i31−i32−1+i31−i321−i321−i32−1+i300−1−i31+i32−1−i31+i321+i321+i32−1−i300
χ1633-1-10001-133-1-10001-1−3+3i32−3+3i321−i321−i32000−1+i321−i32−3−3i32−3−3i321+i321+i32000−1−i321+i3233-1-10001-133-1-10001-1−3+3i32−3+3i321−i321−i32000−1+i321−i32−3−3i32−3−3i321+i321+i32000−1−i321+i32
χ1733-1-1000-1133-1-1000-11−3+3i32−3+3i321−i321−i320001−i32−1+i32−3−3i32−3−3i321+i321+i320001+i32−1−i3233-1-1000-1133-1-1000-11−3+3i32−3+3i321−i321−i320001−i32−1+i32−3−3i32−3−3i321+i321+i320001+i32−1−i32
χ186-3-21000006-3-2100000−3+3i33−3i321−i3−1+i3200000−3−3i33+3i321+i3−1−i32000006-3-21000006-3-2100000−3+3i33−3i321−i3−1+i3200000−3−3i33+3i321+i3−1−i3200000
χ19111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ201111111-1-11111111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321111111-1-11111111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ212222-1-1-1002222-1-1-100−1−i3−1−i3−1−i3−1−i31+i321+i321+i3200−1+i3−1+i3−1+i3−1+i31−i321−i321−i32002222-1-1-1002222-1-1-100−1−i3−1−i3−1−i3−1−i31+i321+i321+i3200−1+i3−1+i3−1+i3−1+i31−i321−i321−i3200
χ222-12-12-1-1002-12-12-1-100−1−i31+i32−1−i31+i32−1−i31+i321+i3200−1+i31−i32−1+i31−i32−1+i31−i321−i32002-12-12-1-1002-12-12-1-100−1−i31+i32−1−i31+i32−1−i31+i321+i3200−1+i31−i32−1+i31−i32−1+i31−i321−i3200
χ232-12-1-12-1002-12-1-12-100−1−i31+i32−1−i31+i321+i32−1−i31+i3200−1+i31−i32−1+i31−i321−i32−1+i31−i32002-12-1-12-1002-12-1-12-100−1−i31+i32−1−i31+i321+i32−1−i31+i3200−1+i31−i32−1+i31−i321−i32−1+i31−i3200
χ242-12-1-1-12002-12-1-1-1200−1−i31+i32−1−i31+i321+i321+i32−1−i300−1+i31−i32−1+i31−i321−i321−i32−1+i3002-12-1-1-12002-12-1-1-1200−1−i31+i32−1−i31+i321+i321+i32−1−i300−1+i31−i32−1+i31−i321−i321−i32−1+i300
χ2533-1-10001-133-1-10001-1−3−3i32−3−3i321+i321+i32000−1−i321+i32−3+3i32−3+3i321−i321−i32000−1+i321−i3233-1-10001-133-1-10001-1−3−3i32−3−3i321+i321+i32000−1−i321+i32−3+3i32−3+3i321−i321−i32000−1+i321−i32
χ2633-1-1000-1133-1-1000-11−3−3i32−3−3i321+i321+i320001+i32−1−i32−3+3i32−3+3i321−i321−i320001−i32−1+i3233-1-1000-1133-1-1000-11−3−3i32−3−3i321+i321+i320001+i32−1−i32−3+3i32−3+3i321−i321−i320001−i32−1+i32
χ276-3-21000006-3-2100000−3−3i33+3i321+i3−1−i3200000−3+3i33−3i321−i3−1+i32000006-3-21000006-3-2100000−3−3i33+3i321+i3−1−i3200000−3+3i33−3i321−i3−1+i3200000
χ28333333333-1-1-1-1-1-1-1-1-1000000000000000000333333333-1-1-1-1-1-1-1-1-1000000000000000000
χ293333333-3-3-1-1-1-1-1-1-1110000000000000000003333333-3-3-1-1-1-1-1-1-111000000000000000000
χ306666-3-3-300-2-2-2-2111000000000000000000006666-3-3-300-2-2-2-211100000000000000000000
χ316-36-36-3-300-21-21-211000000000000000000006-36-36-3-300-21-21-21100000000000000000000
χ326-36-3-36-300-21-211-21000000000000000000006-36-3-36-300-21-211-2100000000000000000000
χ336-36-3-3-3600-21-2111-2000000000000000000006-36-3-3-3600-21-2111-200000000000000000000
χ3499-3-30003-3-3-311000-1100000000000000000099-3-30003-3-3-311000-11000000000000000000
χ3599-3-3000-33-3-3110001-100000000000000000099-3-3000-33-3-3110001-1000000000000000000
χ3618-9-6300000-632-10000000000000000000000018-9-6300000-632-100000000000000000000000
χ37111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ381111111-1-11111111-1-11111111-1-11111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-111
χ392222-1-1-1002222-1-1-1002222-1-1-1002222-1-1-100-2-2-2-211100-2-2-2-211100-2-2-2-211100-2-2-2-211100
χ402-12-12-1-1002-12-12-1-1002-12-12-1-1002-12-12-1-100-21-21-21100-21-21-21100-21-21-21100-21-21-21100
χ412-12-1-12-1002-12-1-12-1002-12-1-12-1002-12-1-12-100-21-211-2100-21-211-2100-21-211-2100-21-211-2100
χ422-12-1-1-12002-12-1-1-12002-12-1-1-12002-12-1-1-1200-21-2111-200-21-2111-200-21-2111-200-21-2111-200
χ4333-1-10001-133-1-10001-133-1-10001-133-1-10001-1-3-311000-11-3-311000-11-3-311000-11-3-311000-11
χ4433-1-1000-1133-1-1000-1133-1-1000-1133-1-1000-11-3-3110001-1-3-3110001-1-3-3110001-1-3-3110001-1
χ456-3-21000006-3-21000006-3-21000006-3-2100000-632-100000-632-100000-632-100000-632-100000
χ46111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32
χ471111111-1-11111111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32-1-1-1-1-1-1-111-1-1-1-1-1-1-1111−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ482222-1-1-1002222-1-1-100−1+i3−1+i3−1+i3−1+i31−i321−i321−i3200−1−i3−1−i3−1−i3−1−i31+i321+i321+i3200-2-2-2-211100-2-2-2-2111001−i31−i31−i31−i3−1+i32−1+i32−1+i32001+i31+i31+i31+i3−1−i32−1−i32−1−i3200
χ492-12-12-1-1002-12-12-1-100−1+i31−i32−1+i31−i32−1+i31−i321−i3200−1−i31+i32−1−i31+i32−1−i31+i321+i3200-21-21-21100-21-21-211001−i3−1+i321−i3−1+i321−i3−1+i32−1+i32001+i3−1−i321+i3−1−i321+i3−1−i32−1−i3200
χ502-12-1-12-1002-12-1-12-100−1+i31−i32−1+i31−i321−i32−1+i31−i3200−1−i31+i32−1−i31+i321+i32−1−i31+i3200-21-211-2100-21-211-21001−i3−1+i321−i3−1+i32−1+i321−i3−1+i32001+i3−1−i321+i3−1−i32−1−i321+i3−1−i3200
χ512-12-1-1-12002-12-1-1-1200−1+i31−i32−1+i31−i321−i321−i32−1+i300−1−i31+i32−1−i31+i321+i321+i32−1−i300-21-2111-200-21-2111-2001−i3−1+i321−i3−1+i32−1+i32−1+i321−i3001+i3−1−i321+i3−1−i32−1−i32−1−i321+i300
χ5233-1-10001-133-1-10001-1−3+3i32−3+3i321−i321−i32000−1+i321−i32−3−3i32−3−3i321+i321+i32000−1−i321+i32-3-311000-11-3-311000-113−3i323−3i32−1+i32−1+i320001−i32−1+i323+3i323+3i32−1−i32−1−i320001+i32−1−i32
χ5333-1-1000-1133-1-1000-11−3+3i32−3+3i321−i321−i320001−i32−1+i32−3−3i32−3−3i321+i321+i320001+i32−1−i32-3-3110001-1-3-3110001-13−3i323−3i32−1+i32−1+i32000−1+i321−i323+3i323+3i32−1−i32−1−i32000−1−i321+i32
χ546-3-21000006-3-2100000−3+3i33−3i321−i3−1+i3200000−3−3i33+3i321+i3−1−i3200000-632-100000-632-1000003−3i3−3+3i32−1+i31−i32000003+3i3−3−3i32−1−i31+i3200000
χ55111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32
χ561111111-1-11111111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32-1-1-1-1-1-1-111-1-1-1-1-1-1-1111+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32
χ572222-1-1-1002222-1-1-100−1−i3−1−i3−1−i3−1−i31+i321+i321+i3200−1+i3−1+i3−1+i3−1+i31−i321−i321−i3200-2-2-2-211100-2-2-2-2111001+i31+i31+i31+i3−1−i32−1−i32−1−i32001−i31−i31−i31−i3−1+i32−1+i32−1+i3200
χ582-12-12-1-1002-12-12-1-100−1−i31+i32−1−i31+i32−1−i31+i321+i3200−1+i31−i32−1+i31−i32−1+i31−i321−i3200-21-21-21100-21-21-211001+i3−1−i321+i3−1−i321+i3−1−i32−1−i32001−i3−1+i321−i3−1+i321−i3−1+i32−1+i3200
χ592-12-1-12-1002-12-1-12-100−1−i31+i32−1−i31+i321+i32−1−i31+i3200−1+i31−i32−1+i31−i321−i32−1+i31−i3200-21-211-2100-21-211-21001+i3−1−i321+i3−1−i32−1−i321+i3−1−i32001−i3−1+i321−i3−1+i32−1+i321−i3−1+i3200
χ602-12-1-1-12002-12-1-1-1200−1−i31+i32−1−i31+i321+i321+i32−1−i300−1+i31−i32−1+i31−i321−i321−i32−1+i300-21-2111-200-21-2111-2001+i3−1−i321+i3−1−i32−1−i32−1−i321+i3001−i3−1+i321−i3−1+i32−1+i32−1+i321−i300
χ6133-1-10001-133-1-10001-1−3−3i32−3−3i321+i321+i32000−1−i321+i32−3+3i32−3+3i321−i321−i32000−1+i321−i32-3-311000-11-3-311000-113+3i323+3i32−1−i32−1−i320001+i32−1−i323−3i323−3i32−1+i32−1+i320001−i32−1+i32
χ6233-1-1000-1133-1-1000-11−3−3i32−3−3i321+i321+i320001+i32−1−i32−3+3i32−3+3i321−i321−i320001−i32−1+i32-3-3110001-1-3-3110001-13+3i323+3i32−1−i32−1−i32000−1−i321+i323−3i323−3i32−1+i32−1+i32000−1+i321−i32
χ636-3-21000006-3-2100000−3−3i33+3i321+i3−1−i3200000−3+3i33−3i321−i3−1+i3200000-632-100000-632-1000003+3i3−3−3i32−1−i31+i32000003−3i3−3+3i32−1+i31−i3200000
χ64333333333-1-1-1-1-1-1-1-1-1000000000000000000-3-3-3-3-3-3-3-3-3111111111000000000000000000
χ653333333-3-3-1-1-1-1-1-1-111000000000000000000-3-3-3-3-3-3-3331111111-1-1000000000000000000
χ666666-3-3-300-2-2-2-211100000000000000000000-6-6-6-6333002222-1-1-100000000000000000000
χ676-36-36-3-300-21-21-21100000000000000000000-63-63-633002-12-12-1-100000000000000000000
χ686-36-3-36-300-21-211-2100000000000000000000-63-633-63002-12-1-12-100000000000000000000
χ696-36-3-3-3600-21-2111-200000000000000000000-63-6333-6002-12-1-1-1200000000000000000000
χ7099-3-30003-3-3-311000-11000000000000000000-9-933000-3333-1-10001-1000000000000000000
χ7199-3-3000-33-3-3110001-1000000000000000000-9-9330003-333-1-1000-11000000000000000000
χ7218-9-6300000-632-100000000000000000000000-1896-3000006-3-2100000000000000000000000

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