Finite Group Databasebeta

← Group #72252806

Character table — Group #72252806

Order 5184.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11444488161616161616161618181818363636363636363636363636727281811621623243243243241144448816161616161616161818181836363636363636363636363672728181162162324324324324
order1233663633336666448812121212242424242424242412122288444422666666666666664488121212122424242424242424121222884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111111111111111111111111111111111111111-1-1-1-1
χ3111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1
χ4111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111-1111111111111111-1-1-1-1-1-1i−ii−i1111111111111111-1111111111111111-1-1-1-1-1-1i−ii−i
χ61111111111111111-1111111111111111-1-1-1-1-1-1−ii−ii1111111111111111-1111111111111111-1-1-1-1-1-1−ii−ii
χ71111111111111111-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111i−i−ii1111111111111111-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111i−i−ii
χ81111111111111111-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111−iii−i1111111111111111-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111−iii−i
χ922222222222222222-200-2-2-2-20000000022-2-200000022222222222222222-200-2-2-2-20000000022-2-2000000
χ102222222222222222-2-200-2-2-2-200000000-2-2220000002222222222222222-2-200-2-2-2-200000000-2-222000000
χ112-222-2-22-22222-2-2-2-200i2−i20000i2i2i2i2−i2−i2−i2−i2002-2i2−i200002-222-2-22-22222-2-2-2-200i2−i20000i2i2i2i2−i2−i2−i2−i2002-2i2−i20000
χ122-222-2-22-22222-2-2-2-200i2−i20000i2i2i2i2−i2−i2−i2−i200-22−i2i200002-222-2-22-22222-2-2-2-200i2−i20000i2i2i2i2−i2−i2−i2−i200-22−i2i20000
χ132-222-2-22-22222-2-2-2-200−i2i20000−i2−i2−i2−i2i2i2i2i2002-2−i2i200002-222-2-22-22222-2-2-2-200−i2i20000−i2−i2−i2−i2i2i2i2i2002-2−i2i20000
χ142-222-2-22-22222-2-2-2-200−i2i20000−i2−i2−i2−i2i2i2i2i200-22i2−i200002-222-2-22-22222-2-2-2-200−i2i20000−i2−i2−i2−i2i2i2i2i200-22i2−i20000
χ15441-21-24411-2-211-2-2044411-2-211-2-211-2-20000000000441-21-24411-2-211-2-2044411-2-211-2-211-2-20000000000
χ16441-21-24411-2-211-2-204-4-411-2-2-1-122-1-1220000000000441-21-24411-2-211-2-204-4-411-2-2-1-122-1-1220000000000
χ17441-21-24411-2-211-2-20-400-1-1223i−3i003i−3i000000000000441-21-24411-2-211-2-20-400-1-1223i−3i003i−3i000000000000
χ18441-21-24411-2-211-2-20-400-1-122−3i3i00−3i3i000000000000441-21-24411-2-211-2-20-400-1-122−3i3i00−3i3i000000000000
χ1944-21-2144-2-211-2-2110444-2-211-2-211-2-211000000000044-21-2144-2-211-2-2110444-2-211-2-211-2-2110000000000
χ2044-21-2144-2-211-2-21104-4-4-2-21122-1-122-1-1000000000044-21-2144-2-211-2-21104-4-4-2-21122-1-122-1-10000000000
χ2144-21-2144-2-211-2-2110-40022-1-1003i−3i003i−3i000000000044-21-2144-2-211-2-2110-40022-1-1003i−3i003i−3i0000000000
χ2244-21-2144-2-211-2-2110-40022-1-100−3i3i00−3i3i000000000044-21-2144-2-211-2-2110-40022-1-100−3i3i00−3i3i0000000000
χ234-41-2-124-411-2-2-1-122002i2−2i23i−3i002ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i200000000004-41-2-124-411-2-2-1-122002i2−2i23i−3i002ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i20000000000
χ244-41-2-124-411-2-2-1-122002i2−2i2−3i3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i200000000004-41-2-124-411-2-2-1-122002i2−2i2−3i3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i20000000000
χ254-41-2-124-411-2-2-1-12200−2i22i23i−3i00−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i200000000004-41-2-124-411-2-2-1-12200−2i22i23i−3i00−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i20000000000
χ264-41-2-124-411-2-2-1-12200−2i22i2−3i3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i200000000004-41-2-124-411-2-2-1-12200−2i22i2−3i3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i20000000000
χ274-4-212-14-4-2-21122-1-1002i2−2i2003i−3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ300000000004-4-212-14-4-2-21122-1-1002i2−2i2003i−3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ30000000000
χ284-4-212-14-4-2-21122-1-1002i2−2i200−3i3i−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ300000000004-4-212-14-4-2-21122-1-1002i2−2i200−3i3i−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ30000000000
χ294-4-212-14-4-2-21122-1-100−2i22i2003i−3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ300000000004-4-212-14-4-2-21122-1-100−2i22i2003i−3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ30000000000
χ304-4-212-14-4-2-21122-1-100−2i22i200−3i3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ300000000004-4-212-14-4-2-21122-1-100−2i22i200−3i3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ30000000000
χ31888888-1-1-1-1-1-1-1-1-1-18000000000000000-1-100000000888888-1-1-1-1-1-1-1-1-1-18000000000000000-1-100000000
χ32888888-1-1-1-1-1-1-1-1-1-1-80000000000000001100000000888888-1-1-1-1-1-1-1-1-1-1-80000000000000001100000000
χ338-888-8-8-11-1-1-1-1111100000000000000003i−3i000000008-888-8-8-11-1-1-1-1111100000000000000003i−3i00000000
χ348-888-8-8-11-1-1-1-111110000000000000000−3i3i000000008-888-8-8-11-1-1-1-111110000000000000000−3i3i00000000
χ3516164-84-8-2-24-5114-5110000000000000000000000000016164-84-8-2-24-5114-51100000000000000000000000000
χ3616164-84-8-2-2-5411-54110000000000000000000000000016164-84-8-2-2-5411-541100000000000000000000000000
χ371616-84-84-2-2114-5114-5000000000000000000000000001616-84-84-2-2114-5114-500000000000000000000000000
χ381616-84-84-2-211-5411-54000000000000000000000000001616-84-84-2-211-5411-5400000000000000000000000000
χ3916-164-8-48-224-511-45-1-10000000000000000000000000016-164-8-48-224-511-45-1-100000000000000000000000000
χ4016-164-8-48-22-54115-4-1-10000000000000000000000000016-164-8-48-22-54115-4-1-100000000000000000000000000
χ4116-16-848-4-22114-5-1-1-450000000000000000000000000016-16-848-4-22114-5-1-1-4500000000000000000000000000
χ4216-16-848-4-2211-54-1-15-40000000000000000000000000016-16-848-4-2211-54-1-15-400000000000000000000000000
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
χ45111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-111
χ46111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1
χ471111111111111111-1111111111111111-1-1-1-1-1-1i−ii−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−ii−ii
χ481111111111111111-1111111111111111-1-1-1-1-1-1−ii−ii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111i−ii−i
χ491111111111111111-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111i−i−ii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1111111111111-1-1−iii−i
χ501111111111111111-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-111−iii−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1111111111111-1-1i−i−ii
χ5122222222222222222-200-2-2-2-20000000022-2-2000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2200222200000000-2-222000000
χ522222222222222222-2-200-2-2-2-200000000-2-222000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2220022220000000022-2-2000000
χ532-222-2-22-22222-2-2-2-200i2−i20000i2i2i2i2−i2−i2−i2−i2002-2i2−i20000-22-2-222-22-2-2-2-2222200−i2i20000−i2−i2−i2−i2i2i2i2i200-22−i2i20000
χ542-222-2-22-22222-2-2-2-200i2−i20000i2i2i2i2−i2−i2−i2−i200-22−i2i20000-22-2-222-22-2-2-2-2222200−i2i20000−i2−i2−i2−i2i2i2i2i2002-2i2−i20000
χ552-222-2-22-22222-2-2-2-200−i2i20000−i2−i2−i2−i2i2i2i2i2002-2−i2i20000-22-2-222-22-2-2-2-2222200i2−i20000i2i2i2i2−i2−i2−i2−i200-22i2−i20000
χ562-222-2-22-22222-2-2-2-200−i2i20000−i2−i2−i2−i2i2i2i2i200-22i2−i20000-22-2-222-22-2-2-2-2222200i2−i20000i2i2i2i2−i2−i2−i2−i2002-2−i2i20000
χ57441-21-24411-2-211-2-2044411-2-211-2-211-2-20000000000-4-4-12-12-4-4-1-122-1-1220-4-4-4-1-122-1-122-1-1220000000000
χ58441-21-24411-2-211-2-204-4-411-2-2-1-122-1-1220000000000-4-4-12-12-4-4-1-122-1-1220-444-1-12211-2-211-2-20000000000
χ59441-21-24411-2-211-2-20-400-1-1223i−3i003i−3i000000000000-4-4-12-12-4-4-1-122-1-122040011-2-2−3i3i00−3i3i000000000000
χ60441-21-24411-2-211-2-20-400-1-122−3i3i00−3i3i000000000000-4-4-12-12-4-4-1-122-1-122040011-2-23i−3i003i−3i000000000000
χ6144-21-2144-2-211-2-2110444-2-211-2-211-2-2110000000000-4-42-12-1-4-422-1-122-1-10-4-4-422-1-122-1-122-1-10000000000
χ6244-21-2144-2-211-2-21104-4-4-2-21122-1-122-1-10000000000-4-42-12-1-4-422-1-122-1-10-44422-1-1-2-211-2-2110000000000
χ6344-21-2144-2-211-2-2110-40022-1-1003i−3i003i−3i0000000000-4-42-12-1-4-422-1-122-1-10400-2-21100−3i3i00−3i3i0000000000
χ6444-21-2144-2-211-2-2110-40022-1-100−3i3i00−3i3i0000000000-4-42-12-1-4-422-1-122-1-10400-2-211003i−3i003i−3i0000000000
χ654-41-2-124-411-2-2-1-122002i2−2i23i−3i002ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i20000000000-44-121-2-44-1-12211-2-200−2i22i2−3i3i00−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i20000000000
χ664-41-2-124-411-2-2-1-122002i2−2i2−3i3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i20000000000-44-121-2-44-1-12211-2-200−2i22i23i−3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i20000000000
χ674-41-2-124-411-2-2-1-12200−2i22i23i−3i00−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i20000000000-44-121-2-44-1-12211-2-2002i2−2i2−3i3i002ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i20000000000
χ684-41-2-124-411-2-2-1-12200−2i22i2−3i3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i20000000000-44-121-2-44-1-12211-2-2002i2−2i23i−3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i20000000000
χ694-4-212-14-4-2-21122-1-1002i2−2i2003i−3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ30000000000-442-1-21-4422-1-1-2-21100−2i22i200−3i3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ30000000000
χ704-4-212-14-4-2-21122-1-1002i2−2i200−3i3i−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ30000000000-442-1-21-4422-1-1-2-21100−2i22i2003i−3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ30000000000
χ714-4-212-14-4-2-21122-1-100−2i22i2003i−3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ30000000000-442-1-21-4422-1-1-2-211002i2−2i200−3i3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ30000000000
χ724-4-212-14-4-2-21122-1-100−2i22i200−3i3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ30000000000-442-1-21-4422-1-1-2-211002i2−2i2003i−3i−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ30000000000
χ73888888-1-1-1-1-1-1-1-1-1-18000000000000000-1-100000000-8-8-8-8-8-81111111111-80000000000000001100000000
χ74888888-1-1-1-1-1-1-1-1-1-1-80000000000000001100000000-8-8-8-8-8-811111111118000000000000000-1-100000000
χ758-888-8-8-11-1-1-1-1111100000000000000003i−3i00000000-88-8-8881-11111-1-1-1-10000000000000000−3i3i00000000
χ768-888-8-8-11-1-1-1-111110000000000000000−3i3i00000000-88-8-8881-11111-1-1-1-100000000000000003i−3i00000000
χ7716164-84-8-2-24-5114-51100000000000000000000000000-16-16-48-4822-45-1-1-45-1-100000000000000000000000000
χ7816164-84-8-2-2-5411-541100000000000000000000000000-16-16-48-48225-4-1-15-4-1-100000000000000000000000000
χ791616-84-84-2-2114-5114-500000000000000000000000000-16-168-48-422-1-1-45-1-1-4500000000000000000000000000
χ801616-84-84-2-211-5411-5400000000000000000000000000-16-168-48-422-1-15-4-1-15-400000000000000000000000000
χ8116-164-8-48-224-511-45-1-100000000000000000000000000-1616-484-82-2-45-1-14-51100000000000000000000000000
χ8216-164-8-48-22-54115-4-1-100000000000000000000000000-1616-484-82-25-4-1-1-541100000000000000000000000000
χ8316-16-848-4-22114-5-1-1-4500000000000000000000000000-16168-4-842-2-1-1-45114-500000000000000000000000000
χ8416-16-848-4-2211-54-1-15-400000000000000000000000000-16168-4-842-2-1-15-411-5400000000000000000000000000

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