Finite Group Databasebeta

← Group #11724520

Character table — Group #11724520

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size112222244444444444444444444444499181818181854545454112222244444444444444444444444499181818181854545454
order12236663333336666666666666666664441212121288882226666666666666666666666666666444121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111111111111111111111111111111111111111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1ii−i−i1111111111111111111111111111111-1-1-1-1-1-1-1ii−i−i
χ41111111111111111111111111111111-1-1-1-1-1-1-1−i−iii1111111111111111111111111111111-1-1-1-1-1-1-1−i−iii
χ511-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11-11-111-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11-11-1
χ611-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-11-1111-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-11-11
χ711-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111i−i−ii11-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111i−i−ii
χ811-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111−iii−i11-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111−iii−i
χ9222-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-10000222-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-10000
χ10222-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-211110000222-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-211110000
χ1122-2-111-122-1-1-1-122-1-1-1-1-2-2-2-21111111122-2-1-111000022-2-111-122-1-1-1-122-1-1-1-1-2-2-2-21111111122-2-1-1110000
χ1222-2-111-122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2211-1-1000022-2-111-122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2211-1-10000
χ132-20200-2222222-2-2-2-2-2-20000000000002i−2i02i−2i0000002-20200-2222222-2-2-2-2-2-20000000000002i−2i02i−2i000000
χ142-20200-2222222-2-2-2-2-2-2000000000000−2i2i0−2i2i0000002-20200-2222222-2-2-2-2-2-2000000000000−2i2i0−2i2i000000
χ152-20-1−i3i3122-1-1-1-1-2-211110000−i3−i3−i3−i3i3i3i3i32i−2i0−ii3−300002-20-1−i3i3122-1-1-1-1-2-211110000−i3−i3−i3−i3i3i3i3i32i−2i0−ii3−30000
χ162-20-1−i3i3122-1-1-1-1-2-211110000−i3−i3−i3−i3i3i3i3i3−2i2i0i−i−3300002-20-1−i3i3122-1-1-1-1-2-211110000−i3−i3−i3−i3i3i3i3i3−2i2i0i−i−330000
χ172-20-1i3−i3122-1-1-1-1-2-211110000i3i3i3i3−i3−i3−i3−i32i−2i0−ii−3300002-20-1i3−i3122-1-1-1-1-2-211110000i3i3i3i3−i3−i3−i3−i32i−2i0−ii−330000
χ182-20-1i3−i3122-1-1-1-1-2-211110000i3i3i3i3−i3−i3−i3−i3−2i2i0i−i3−300002-20-1i3−i3122-1-1-1-1-2-211110000i3i3i3i3−i3−i3−i3−i3−2i2i0i−i3−30000
χ1944444441-211-2-21-211-2-211-2-211-2-211-2-20000000000044444441-211-2-21-211-2-211-2-211-2-211-2-200000000000
χ204444444-21-2-211-21-2-211-2-211-2-211-2-211000000000004444444-21-2-211-21-2-211-2-211-2-211-2-21100000000000
χ21444-2-2-2-21-2−1−3i32−1+3i32111-2−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1−3i32−1+3i321100000000000444-2-2-2-21-2−1−3i32−1+3i32111-2−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1−3i32−1+3i321100000000000
χ22444-2-2-2-21-2−1+3i32−1−3i32111-2−1+3i32−1−3i321111-2-2−1+3i32−1−3i3211−1+3i32−1−3i321100000000000444-2-2-2-21-2−1+3i32−1−3i32111-2−1+3i32−1−3i321111-2-2−1+3i32−1−3i3211−1+3i32−1−3i321100000000000
χ23444-2-2-2-2-2111−1−3i32−1+3i32-2111−1−3i32−1+3i32-2-21111−1−3i32−1+3i3211−1−3i32−1+3i3200000000000444-2-2-2-2-2111−1−3i32−1+3i32-2111−1−3i32−1+3i32-2-21111−1−3i32−1+3i3211−1−3i32−1+3i3200000000000
χ24444-2-2-2-2-2111−1+3i32−1−3i32-2111−1+3i32−1−3i32-2-21111−1+3i32−1−3i3211−1+3i32−1−3i3200000000000444-2-2-2-2-2111−1+3i32−1−3i32-2111−1+3i32−1−3i32-2-21111−1+3i32−1−3i3211−1+3i32−1−3i3200000000000
χ2544-44-4-441-211-2-21-211-2-2-1-122-1-122-1-1220000000000044-44-4-441-211-2-21-211-2-2-1-122-1-122-1-12200000000000
χ2644-44-4-44-21-2-211-21-2-21122-1-122-1-122-1-10000000000044-44-4-44-21-2-211-21-2-21122-1-122-1-122-1-100000000000
χ2744-4-222-21-2−1−3i32−1+3i32111-2−1−3i32−1+3i3211-1-1221+3i321−3i32-1-11+3i321−3i32-1-10000000000044-4-222-21-2−1−3i32−1+3i32111-2−1−3i32−1+3i3211-1-1221+3i321−3i32-1-11+3i321−3i32-1-100000000000
χ2844-4-222-21-2−1+3i32−1−3i32111-2−1+3i32−1−3i3211-1-1221−3i321+3i32-1-11−3i321+3i32-1-10000000000044-4-222-21-2−1+3i32−1−3i32111-2−1+3i32−1−3i3211-1-1221−3i321+3i32-1-11−3i321+3i32-1-100000000000
χ2944-4-222-2-2111−1−3i32−1+3i32-2111−1−3i32−1+3i3222-1-1-1-11+3i321−3i32-1-11+3i321−3i320000000000044-4-222-2-2111−1−3i32−1+3i32-2111−1−3i32−1+3i3222-1-1-1-11+3i321−3i32-1-11+3i321−3i3200000000000
χ3044-4-222-2-2111−1+3i32−1−3i32-2111−1+3i32−1−3i3222-1-1-1-11−3i321+3i32-1-11−3i321+3i320000000000044-4-222-2-2111−1+3i32−1−3i32-2111−1+3i32−1−3i3222-1-1-1-11−3i321+3i32-1-11−3i321+3i3200000000000
χ314-40400-41-211-2-2-12-1-1223-3003-300-3300000000000004-40400-41-211-2-2-12-1-1223-3003-300-330000000000000
χ324-40400-41-211-2-2-12-1-122-3300-33003-300000000000004-40400-41-211-2-2-12-1-122-3300-33003-30000000000000
χ334-40400-4-21-2-2112-122-1-1003-3003-300-33000000000004-40400-4-21-2-2112-122-1-1003-3003-300-3300000000000
χ344-40400-4-21-2-2112-122-1-100-3300-33003-3000000000004-40400-4-21-2-2112-122-1-100-3300-33003-300000000000
χ354-40-2−2i32i321-2−1−3i32−1+3i3211-121+3i321−3i32-1-13-300−3−i323−i32i3i33+i32−3+i32−i3−i3000000000004-40-2−2i32i321-2−1−3i32−1+3i3211-121+3i321−3i32-1-13-300−3−i323−i32i3i33+i32−3+i32−i3−i300000000000
χ364-40-2−2i32i321-2−1+3i32−1−3i3211-121−3i321+3i32-1-1-33003−i32−3−i32i3i3−3+i323+i32−i3−i3000000000004-40-2−2i32i321-2−1+3i32−1−3i3211-121−3i321+3i32-1-1-33003−i32−3−i32i3i3−3+i323+i32−i3−i300000000000
χ374-40-2−2i32i32-2111−1−3i32−1+3i322-1-1-11+3i321−3i32003-3i3i3−3−i323−i32−i3−i33+i32−3+i32000000000004-40-2−2i32i32-2111−1−3i32−1+3i322-1-1-11+3i321−3i32003-3i3i3−3−i323−i32−i3−i33+i32−3+i3200000000000
χ384-40-2−2i32i32-2111−1+3i32−1−3i322-1-1-11−3i321+3i3200-33i3i33−i32−3−i32−i3−i3−3+i323+i32000000000004-40-2−2i32i32-2111−1+3i32−1−3i322-1-1-11−3i321+3i3200-33i3i33−i32−3−i32−i3−i3−3+i323+i3200000000000
χ394-40-22i3−2i321-2−1−3i32−1+3i3211-121+3i321−3i32-1-1-33003+i32−3+i32−i3−i3−3−i323−i32i3i3000000000004-40-22i3−2i321-2−1−3i32−1+3i3211-121+3i321−3i32-1-1-33003+i32−3+i32−i3−i3−3−i323−i32i3i300000000000
χ404-40-22i3−2i321-2−1+3i32−1−3i3211-121−3i321+3i32-1-13-300−3+i323+i32−i3−i33−i32−3−i32i3i3000000000004-40-22i3−2i321-2−1+3i32−1−3i3211-121−3i321+3i32-1-13-300−3+i323+i32−i3−i33−i32−3−i32i3i300000000000
χ414-40-22i3−2i32-2111−1−3i32−1+3i322-1-1-11+3i321−3i3200-33−i3−i33+i32−3+i32i3i3−3−i323−i32000000000004-40-22i3−2i32-2111−1−3i32−1+3i322-1-1-11+3i321−3i3200-33−i3−i33+i32−3+i32i3i3−3−i323−i3200000000000
χ424-40-22i3−2i32-2111−1+3i32−1−3i322-1-1-11−3i321+3i32003-3−i3−i3−3+i323+i32i3i33−i32−3−i32000000000004-40-22i3−2i32-2111−1+3i32−1−3i322-1-1-11−3i321+3i32003-3−i3−i3−3+i323+i32i3i33−i32−3−i3200000000000
χ43111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ451111111111111111111111111111111-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111−i−iii
χ461111111111111111111111111111111-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111ii−i−i
χ4711-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11-11-1-1-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11-1-111-11-11
χ4811-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-11-11-1-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11-1-1111-11-1
χ4911-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111i−i−ii-1-11-111-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-111-1-1−iii−i
χ5011-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111−iii−i-1-11-111-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-111-1-1i−i−ii
χ51222-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-10000-2-2-21111-2-21111-2-21111-2-2-2-211111111-2-2-211110000
χ52222-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-211110000-2-2-21111-2-21111-2-21111-2-2-2-211111111222-1-1-1-10000
χ5322-2-111-122-1-1-1-122-1-1-1-1-2-2-2-21111111122-2-1-1110000-2-221-1-11-2-21111-2-211112222-1-1-1-1-1-1-1-1-2-2211-1-10000
χ5422-2-111-122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2211-1-10000-2-221-1-11-2-21111-2-211112222-1-1-1-1-1-1-1-122-2-1-1110000
χ552-20200-2222222-2-2-2-2-2-20000000000002i−2i02i−2i000000-220-2002-2-2-2-2-2-2222222000000000000−2i2i0−2i2i000000
χ562-20200-2222222-2-2-2-2-2-2000000000000−2i2i0−2i2i000000-220-2002-2-2-2-2-2-22222220000000000002i−2i02i−2i000000
χ572-20-1−i3i3122-1-1-1-1-2-211110000−i3−i3−i3−i3i3i3i3i32i−2i0−ii3−30000-2201i3−i3-1-2-2111122-1-1-1-10000i3i3i3i3−i3−i3−i3−i3−2i2i0i−i−330000
χ582-20-1−i3i3122-1-1-1-1-2-211110000−i3−i3−i3−i3i3i3i3i3−2i2i0i−i−330000-2201i3−i3-1-2-2111122-1-1-1-10000i3i3i3i3−i3−i3−i3−i32i−2i0−ii3−30000
χ592-20-1i3−i3122-1-1-1-1-2-211110000i3i3i3i3−i3−i3−i3−i32i−2i0−ii−330000-2201−i3i3-1-2-2111122-1-1-1-10000−i3−i3−i3−i3i3i3i3i3−2i2i0i−i3−30000
χ602-20-1i3−i3122-1-1-1-1-2-211110000i3i3i3i3−i3−i3−i3−i3−2i2i0i−i3−30000-2201−i3i3-1-2-2111122-1-1-1-10000−i3−i3−i3−i3i3i3i3i32i−2i0−ii−330000
χ6144444441-211-2-21-211-2-211-2-211-2-211-2-200000000000-4-4-4-4-4-4-4-12-1-122-12-1-122-1-122-1-122-1-12200000000000
χ624444444-21-2-211-21-2-211-2-211-2-211-2-21100000000000-4-4-4-4-4-4-42-122-1-12-122-1-122-1-122-1-122-1-100000000000
χ63444-2-2-2-21-2−1−3i32−1+3i32111-2−1−3i32−1+3i321111-2-2−1−3i32−1+3i3211−1−3i32−1+3i321100000000000-4-4-42222-121+3i321−3i32-1-1-121+3i321−3i32-1-1-1-1221+3i321−3i32-1-11+3i321−3i32-1-100000000000
χ64444-2-2-2-21-2−1+3i32−1−3i32111-2−1+3i32−1−3i321111-2-2−1+3i32−1−3i3211−1+3i32−1−3i321100000000000-4-4-42222-121−3i321+3i32-1-1-121−3i321+3i32-1-1-1-1221−3i321+3i32-1-11−3i321+3i32-1-100000000000
χ65444-2-2-2-2-2111−1−3i32−1+3i32-2111−1−3i32−1+3i32-2-21111−1−3i32−1+3i3211−1−3i32−1+3i3200000000000-4-4-422222-1-1-11+3i321−3i322-1-1-11+3i321−3i3222-1-1-1-11+3i321−3i32-1-11+3i321−3i3200000000000
χ66444-2-2-2-2-2111−1+3i32−1−3i32-2111−1+3i32−1−3i32-2-21111−1+3i32−1−3i3211−1+3i32−1−3i3200000000000-4-4-422222-1-1-11−3i321+3i322-1-1-11−3i321+3i3222-1-1-1-11−3i321+3i32-1-11−3i321+3i3200000000000
χ6744-44-4-441-211-2-21-211-2-2-1-122-1-122-1-12200000000000-4-44-444-4-12-1-122-12-1-12211-2-211-2-211-2-200000000000
χ6844-44-4-44-21-2-211-21-2-21122-1-122-1-122-1-100000000000-4-44-444-42-122-1-12-122-1-1-2-211-2-211-2-21100000000000
χ6944-4-222-21-2−1−3i32−1+3i32111-2−1−3i32−1+3i3211-1-1221+3i321−3i32-1-11+3i321−3i32-1-100000000000-4-442-2-22-121+3i321−3i32-1-1-121+3i321−3i32-1-111-2-2−1−3i32−1+3i3211−1−3i32−1+3i321100000000000
χ7044-4-222-21-2−1+3i32−1−3i32111-2−1+3i32−1−3i3211-1-1221−3i321+3i32-1-11−3i321+3i32-1-100000000000-4-442-2-22-121−3i321+3i32-1-1-121−3i321+3i32-1-111-2-2−1+3i32−1−3i3211−1+3i32−1−3i321100000000000
χ7144-4-222-2-2111−1−3i32−1+3i32-2111−1−3i32−1+3i3222-1-1-1-11+3i321−3i32-1-11+3i321−3i3200000000000-4-442-2-222-1-1-11+3i321−3i322-1-1-11+3i321−3i32-2-21111−1−3i32−1+3i3211−1−3i32−1+3i3200000000000
χ7244-4-222-2-2111−1+3i32−1−3i32-2111−1+3i32−1−3i3222-1-1-1-11−3i321+3i32-1-11−3i321+3i3200000000000-4-442-2-222-1-1-11−3i321+3i322-1-1-11−3i321+3i32-2-21111−1+3i32−1−3i3211−1+3i32−1−3i3200000000000
χ734-40400-41-211-2-2-12-1-1223-3003-300-330000000000000-440-4004-12-1-1221-211-2-2-3300-33003-30000000000000
χ744-40400-41-211-2-2-12-1-122-3300-33003-30000000000000-440-4004-12-1-1221-211-2-23-3003-300-330000000000000
χ754-40400-4-21-2-2112-122-1-1003-3003-300-3300000000000-440-40042-122-1-1-21-2-21100-3300-33003-300000000000
χ764-40400-4-21-2-2112-122-1-100-3300-33003-300000000000-440-40042-122-1-1-21-2-211003-3003-300-3300000000000
χ774-40-2−2i32i321-2−1−3i32−1+3i3211-121+3i321−3i32-1-13-300−3−i323−i32i3i33+i32−3+i32−i3−i300000000000-44022i3−2i3-2-121+3i321−3i32-1-11-2−1−3i32−1+3i3211-33003+i32−3+i32−i3−i3−3−i323−i32i3i300000000000
χ784-40-2−2i32i321-2−1+3i32−1−3i3211-121−3i321+3i32-1-1-33003−i32−3−i32i3i3−3+i323+i32−i3−i300000000000-44022i3−2i3-2-121−3i321+3i32-1-11-2−1+3i32−1−3i32113-300−3+i323+i32−i3−i33−i32−3−i32i3i300000000000
χ794-40-2−2i32i32-2111−1−3i32−1+3i322-1-1-11+3i321−3i32003-3i3i3−3−i323−i32−i3−i33+i32−3+i3200000000000-44022i3−2i3-22-1-1-11+3i321−3i32-2111−1−3i32−1+3i3200-33−i3−i33+i32−3+i32i3i3−3−i323−i3200000000000
χ804-40-2−2i32i32-2111−1+3i32−1−3i322-1-1-11−3i321+3i3200-33i3i33−i32−3−i32−i3−i3−3+i323+i3200000000000-44022i3−2i3-22-1-1-11−3i321+3i32-2111−1+3i32−1−3i32003-3−i3−i3−3+i323+i32i3i33−i32−3−i3200000000000
χ814-40-22i3−2i321-2−1−3i32−1+3i3211-121+3i321−3i32-1-1-33003+i32−3+i32−i3−i3−3−i323−i32i3i300000000000-4402−2i32i3-2-121+3i321−3i32-1-11-2−1−3i32−1+3i32113-300−3−i323−i32i3i33+i32−3+i32−i3−i300000000000
χ824-40-22i3−2i321-2−1+3i32−1−3i3211-121−3i321+3i32-1-13-300−3+i323+i32−i3−i33−i32−3−i32i3i300000000000-4402−2i32i3-2-121−3i321+3i32-1-11-2−1+3i32−1−3i3211-33003−i32−3−i32i3i3−3+i323+i32−i3−i300000000000
χ834-40-22i3−2i32-2111−1−3i32−1+3i322-1-1-11+3i321−3i3200-33−i3−i33+i32−3+i32i3i3−3−i323−i3200000000000-4402−2i32i3-22-1-1-11+3i321−3i32-2111−1−3i32−1+3i32003-3i3i3−3−i323−i32−i3−i33+i32−3+i3200000000000
χ844-40-22i3−2i32-2111−1+3i32−1−3i322-1-1-11−3i321+3i32003-3−i3−i3−3+i323+i32i3i33−i32−3−i3200000000000-4402−2i32i3-22-1-1-11−3i321+3i32-2111−1+3i32−1−3i3200-33i3i33−i32−3−i32−i3−i3−3+i323+i3200000000000

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