Finite Group Databasebeta

← Group #14282801

Character table — Group #14282801

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222333344444888888888888101010101212121212161616161616162020202020202020202020202424242424242430303030404040404040404040606060606060606080120
order12223666444445101010412152020202020203030302244420202020126060606060604444668888121242020202020204444212121212242424244444888864
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ311111111111111111111111111111-1-1-1-1111111111111ii−i−i-1-1ii−i−i-1-11111111-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i-1-1
χ411111111111111111111111111111-1-1-1-1111111111111−i−iii-1-1−i−iii-1-11111111-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii-1-1
χ511111111111111111-111-1-1-1-111111111111111-111-1-1-1-1111111-1-1-1-111-111-1-1-1-11111-11111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111-111-1-1-1-111111111111111-111-1-1-1-1-1-1-1-111111111-111-1-1-1-11111-1-1-1-1-11111-1-1-1-11111-1-1
χ711111111111111111-111-1-1-1-111111-1-1-1-111111-111-1-1-1-1ii−i−i-1-1−i−iii-1-1-111-1-1-1-1-1-1-1-11ii−i−i−i−iiiii−i−i−i−iii11
χ811111111111111111-111-1-1-1-111111-1-1-1-111111-111-1-1-1-1−i−iii-1-1ii−i−i-1-1-111-1-1-1-1-1-1-1-11−i−iiiii−i−i−i−iiiii−i−i11
χ911111111-1-1-1-1111111111111111111111-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-1
χ1011111111-1-1-1-1111111111111111111111-1-1-1-1-11111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111-1
χ1111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-11111111ii−i−i-1-1ii−i−i-1-1-1-1-1-1-1-1-11111-1ii−i−iii−i−i−i−iii−i−iii-11
χ1211111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-11111111−i−iii-1-1−i−iii-1-1-1-1-1-1-1-1-11111-1−i−iii−i−iiiii−i−iii−i−i-11
χ1311111111-1-1-1-111111-111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111-1-11111-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11
χ1411111111-1-1-1-111111-111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11
χ1511111111-1-1-1-111111-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i-1-1−i−iii-1-11-1-1111111111ii−i−i−i−iii−i−iiiii−i−i1-1
χ1611111111-1-1-1-111111-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1−i−iii-1-1ii−i−i-1-11-1-1111111111−i−iiiii−i−iii−i−i−i−iii1-1
χ17222222222222-222220-220000-2-222222-2-2-222220-2-200000000220000-2-20-2-20000-2-2220000000000000000000
χ18222222222222-222220-220000-2-2222-2-222-222220-2-200000000-2-20000220-2-2000022-2-20000000000000000000
χ1922222222-2-2-2-2-222220-220000-2-222222-2-22-2-2-2-20-2-200000000220000-2-2022000022-2-20000000000000000000
χ2022222222-2-2-2-2-222220-220000-2-2222-2-2222-2-2-2-20-2-200000000-2-20000220220000-2-2220000000000000000000
χ212222-1-1-1-10000222222-1-1222222-1-1-1222200000-1-1-1-1-1-1-12222-1-12222-1-1000000000002-1-1-1-1-1-1-1-100000000-10
χ222222-1-1-1-10000222222-1-1222222-1-1-1222200000-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-2-1-10000000000021111111100000000-10
χ232222-1-1-1-10000222222-1-1222222-1-1-1-2-2-2-200000-1-1-1-1-1-1-12i2i−2i−2i112i2i−2i−2i1100000000000-2−i−iii−i−iii0000000010
χ242222-1-1-1-10000222222-1-1222222-1-1-1-2-2-2-200000-1-1-1-1-1-1-1−2i−2i2i2i11−2i−2i2i2i1100000000000-2ii−i−iii−i−i0000000010
χ252222-1-1-1-1000022222-2-1-1-2-2-2-222-1-1-12222000001-1-111112222-1-1-2-2-2-2-1-100000000000-2-1-1-1-111110000000010
χ262222-1-1-1-1000022222-2-1-1-2-2-2-222-1-1-12222000001-1-11111-2-2-2-2-1-12222-1-100000000000-21111-1-1-1-10000000010
χ272222-1-1-1-1000022222-2-1-1-2-2-2-222-1-1-1-2-2-2-2000001-1-111112i2i−2i−2i11−2i−2i2i2i11000000000002−i−iiiii−i−i00000000-10
χ282222-1-1-1-1000022222-2-1-1-2-2-2-222-1-1-1-2-2-2-2000001-1-11111−2i−2i2i2i112i2i−2i−2i11000000000002ii−i−i−i−iii00000000-10
χ292-22-22-22-22i2i−2i−2i02-22-2002000000-2-222-20002i2i−2i−2i00000000000-222−22−2000000000002i−2i000002−22−20000i2−i2i2−i200
χ302-22-22-22-22i2i−2i−2i02-22-2002000000-2-222-20002i2i−2i−2i00000000000-22−22−22000000000002i−2i00000−22−220000−i2i2−i2i200
χ312-22-22-22-22i2i−2i−2i02-22-2002000000-2-22-220002i2i−2i−2i000000000002-2i2−i2−i2i200000000000−2i2i00000i2−i2−i2i20000−222−200
χ322-22-22-22-22i2i−2i−2i02-22-2002000000-2-22-220002i2i−2i−2i000000000002-2−i2i2i2−i200000000000−2i2i00000−i2i2i2−i200002−2−2200
χ332-22-22-22-2−2i−2i2i2i02-22-2002000000-2-222-2000−2i−2i2i2i00000000000-222−22−200000000000−2i2i000002−22−20000−i2i2−i2i200
χ342-22-22-22-2−2i−2i2i2i02-22-2002000000-2-222-2000−2i−2i2i2i00000000000-22−22−2200000000000−2i2i00000−22−220000i2−i2i2−i200
χ352-22-22-22-2−2i−2i2i2i02-22-2002000000-2-22-22000−2i−2i2i2i000000000002-2i2−i2−i2i2000000000002i−2i00000i2−i2−i2i200002−2−2200
χ362-22-22-22-2−2i−2i2i2i02-22-2002000000-2-22-22000−2i−2i2i2i000000000002-2−i2i2i2−i2000000000002i−2i00000−i2i2i2−i20000−222−200
χ372-2-2222-2-22-22-2022-2-20020000002-2-2002i−2i02-22-200000001+i−1−i1−i−1+i0000002i−2i00000002i−2i0001+i−1−i1−i−1+i00001+i−1−i1−i−1+i000000
χ382-2-2222-2-22-22-2022-2-20020000002-2-2002i−2i02-22-20000000−1−i1+i−1+i1−i0000002i−2i00000002i−2i000−1−i1+i−1+i1−i0000−1−i1+i−1+i1−i000000
χ392-2-2222-2-22-22-2022-2-20020000002-2-200−2i2i02-22-200000001−i−1+i1+i−1−i000000−2i2i0000000−2i2i0001−i−1+i1+i−1−i00001−i−1+i1+i−1−i000000
χ402-2-2222-2-22-22-2022-2-20020000002-2-200−2i2i02-22-20000000−1+i1−i−1−i1+i000000−2i2i0000000−2i2i000−1+i1−i−1−i1+i0000−1+i1−i−1−i1+i000000
χ412-2-2222-2-2-22-22022-2-20020000002-2-2002i−2i0-22-2200000001+i−1−i1−i−1+i0000002i−2i0000000−2i2i0001+i−1−i1−i−1+i0000−1−i1+i−1+i1−i000000
χ422-2-2222-2-2-22-22022-2-20020000002-2-2002i−2i0-22-220000000−1−i1+i−1+i1−i0000002i−2i0000000−2i2i000−1−i1+i−1+i1−i00001+i−1−i1−i−1+i000000
χ432-2-2222-2-2-22-22022-2-20020000002-2-200−2i2i0-22-2200000001−i−1+i1+i−1−i000000−2i2i00000002i−2i0001−i−1+i1+i−1−i0000−1+i1−i−1−i1+i000000
χ442-2-2222-2-2-22-22022-2-20020000002-2-200−2i2i0-22-220000000−1+i1−i−1−i1+i000000−2i2i00000002i−2i000−1+i1−i−1−i1+i00001−i−1+i1+i−1−i000000
χ454444444444444-1-1-1-144-1-1-1-1-1-1-1-1-1-100004-1-1-1-14-1-1-1-1-1-10000000000004-1-1-1-1-1-100000000000000000000000
χ464444444444444-1-1-1-1-44-11111-1-1-1-1-100004-1-1-1-1-4-1-11111000000000000-4-1-1111100000000000000000000000
χ47444444444444-4-1-1-1-10-4-155−5−511-1-1-10000-4-1-1-1-101155−5−500000000000001155−5−500000000000000000000000
χ48444444444444-4-1-1-1-10-4-1−5−55511-1-1-10000-4-1-1-1-1011−5−555000000000000011−5−55500000000000000000000000
χ4944444444-4-4-4-44-1-1-1-144-1-1-1-1-1-1-1-1-1-10000-411114-1-1-1-1-1-1000000000000-411111100000000000000000000000
χ5044444444-4-4-4-44-1-1-1-1-44-11111-1-1-1-1-10000-41111-4-1-11111000000000000411-1-1-1-100000000000000000000000
χ5144444444-4-4-4-4-4-1-1-1-10-4-155−5−511-1-1-100004111101155−5−50000000000000-1-1−5−55500000000000000000000000
χ5244444444-4-4-4-4-4-1-1-1-10-4-1−5−55511-1-1-1000041111011−5−5550000000000000-1-155−5−500000000000000000000000
χ534444-2-2-2-20000-4444402-20000-4-4-2-2-244-4-40000002200000000-2-2000022000000000000000000000000000000
χ544444-2-2-2-20000-4444402-20000-4-4-2-2-2-4-4440000002200000000220000-2-2000000000000000000000000000000
χ5544-4-44-4-444i−4i−4i4i04-4-44004000000-44-4000004i−4i−4i4i0000000000000000000000000000000000000000000000000
χ5644-4-44-4-444i−4i−4i4i0-111-100-1−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ385−51-1100000−iii−i05−5−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000i5−i5−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ3600000000000000000000000
χ5744-4-44-4-444i−4i−4i4i0-111-100-1ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−551-1100000−iii−i0−55ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000−i5i5ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ3600000000000000000000000
χ5844-4-44-4-444i−4i−4i4i0-111-100-1ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ385−51-1100000−iii−i05−5ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000i5−i5ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ3600000000000000000000000
χ5944-4-44-4-444i−4i−4i4i0-111-100-1−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−551-1100000−iii−i0−55−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000−i5i5−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ3600000000000000000000000
χ6044-4-44-4-44−4i4i4i−4i04-4-44004000000-44-400000−4i4i4i−4i0000000000000000000000000000000000000000000000000
χ6144-4-44-4-44−4i4i4i−4i0-111-100-1−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ385−51-1100000i−i−ii05−5−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ380000000000000−i5i5ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ3600000000000000000000000
χ6244-4-44-4-44−4i4i4i−4i0-111-100-1ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−551-1100000i−i−ii0−55ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ380000000000000i5−i5−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ3600000000000000000000000
χ6344-4-44-4-44−4i4i4i−4i0-111-100-1ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ385−51-1100000i−i−ii05−5ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ380000000000000−i5i5−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ3600000000000000000000000
χ6444-4-44-4-44−4i4i4i−4i0-111-100-1−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−551-1100000i−i−ii0−55−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ380000000000000i5−i5ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ3600000000000000000000000
χ654-44-4-22-22000004-44-400-200000022-24-40000000000000000002-222−2222−22000000000000000000−22−220000000000
χ664-44-4-22-22000004-44-400-200000022-24-40000000000000000002-2−2222−22220000000000000000002−22−20000000000
χ674-44-4-22-22000004-44-400-200000022-2-44000000000000000000-222i2−2i2−2i22i2000000000000000000−i2i2i2−i20000000000
χ684-44-4-22-22000004-44-400-200000022-2-44000000000000000000-22−2i22i22i2−2i2000000000000000000i2−i2−i2i20000000000
χ694-4-44-2-2220000044-4-400-2000000-222004i−4i0000000000002+2i−2−2i2−2i−2+2i000000−2i2i000000000000−1−i1+i−1+i1−i00000000000000
χ704-4-44-2-2220000044-4-400-2000000-222004i−4i000000000000−2−2i2+2i−2+2i2−2i000000−2i2i0000000000001+i−1−i1−i−1+i00000000000000
χ714-4-44-2-2220000044-4-400-2000000-22200−4i4i0000000000002−2i−2+2i2+2i−2−2i0000002i−2i000000000000−1+i1−i−1−i1+i00000000000000
χ724-4-44-2-2220000044-4-400-2000000-22200−4i4i000000000000−2+2i2−2i−2−2i2+2i0000002i−2i0000000000001−i−1+i1+i−1−i00000000000000
χ738888-4-4-4-400008-2-2-2-28-41-2-2-2-2-2-2111000000000-4111111000000000000000000000000000000000000000000
χ748888-4-4-4-400008-2-2-2-2-8-412222-2-2111000000000411-1-1-1-1000000000000000000000000000000000000000000
χ758888-4-4-4-40000-8-2-2-2-20412525−25−25221110000000000-1-1−5−555000000000000000000000000000000000000000000
χ768888-4-4-4-40000-8-2-2-2-2041−25−252525221110000000000-1-155−5−5000000000000000000000000000000000000000000
χ7788-8-8-444-4000008-8-8800-40000004-440000000000000000000000000000000000000000000000000000000000
χ7888-8-8-444-400000-222-2001−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ3825−25-11-10000000000−55ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38000000000000000000000000000000000000000000
χ7988-8-8-444-400000-222-20012ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38−2525-11-100000000005−5−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38000000000000000000000000000000000000000000
χ8088-8-8-444-400000-222-20012ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ3825−25-11-10000000000−55−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38000000000000000000000000000000000000000000
χ8188-8-8-444-400000-222-2001−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ38−2525-11-100000000005−5ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38000000000000000000000000000000000000000000
χ828-88-88-88-88i8i−8i−8i0-22-2200-200000022-200000−2i−2i2i2i0000000000000000000000000000000000000000000000000
χ838-88-88-88-8−8i−8i8i8i0-22-2200-200000022-2000002i2i−2i−2i0000000000000000000000000000000000000000000000000
χ848-8-8888-8-88-88-80-2-22200-2000000-22200000-22-220000000000000000000000000000000000000000000000000
χ858-8-8888-8-8-88-880-2-22200-2000000-222000002-22-20000000000000000000000000000000000000000000000000
χ8616-1616-16-88-8800000-44-44002000000-2-220000000000000000000000000000000000000000000000000000000000
χ8716-16-1616-8-88800000-4-4440020000002-2-20000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.