Finite Group Databasebeta

← Group #13104236

Character table — Group #13104236

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67
size11114444444444444444488888888888888882020202040404040404040404040404040404040404050505050100100100100
order12224555510101010101010101010101051010102020202020202020202020204444442020202020202020202020202020202044448888
χ11111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1111111111-1-1111-1-1
χ61111-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-1-1-1-111111111-1-1-1-11-1-11-1-111
χ71111-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11111-1-1-1-1-1-1-1-111111-1-11-1-111
χ81111-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111111-1-1-1-1-1-1-1-11-1-1111-1-1
χ922222222222222222222222222222222222220000000000000000000000-2-2-2-20000
χ102222-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000-222-20000
χ1122-2-202222-2-2-2-2-2-2-2-222222-2-22000000000000000000000000000000000002i−2i02−2i2−i2
χ1222-2-202222-2-2-2-2-2-2-2-222222-2-22000000000000000000000000000000000002i−2i0−22−i2i2
χ1322-2-202222-2-2-2-2-2-2-2-222222-2-2200000000000000000000000000000000000−2i2i02−2−i2i2
χ1422-2-202222-2-2-2-2-2-2-2-222222-2-2200000000000000000000000000000000000−2i2i0−22i2−i2
χ152-22-20222222-2-222-2-2-2-2-2-222-2-2000000000000002-20022-2-2000000000000200-20000
χ162-22-20222222-2-222-2-2-2-2-2-222-2-200000000000000-2200-2-222000000000000200-20000
χ172-22-20222222-2-222-2-2-2-2-2-222-2-20000000000002i−2i0000000000002i2i−2i−2i0000-20020000
χ182-22-20222222-2-222-2-2-2-2-2-222-2-2000000000000−2i2i000000000000−2i−2i2i2i0000-20020000
χ1944444−1+53−523+52−1−5−1+5−1−53−523+523−523+52−1+5−1−5−1+53−523+52−1−5-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−5-1-1-1-1222200−1+52−1−52−1+52−1−520000−1+52−1−52−1+52−1−52000000000000
χ2044444−1+53−523+52−1−5−1+5−1−53−523+523−523+52−1+5−1−5−1+53−523+52−1−5-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−5-1-1-1-1-2-2-2-2001−521+521−521+5200001−521+521−521+52000000000000
χ21444443−52−1−5−1+53+523−523+52−1−5−1+5−1−5−1+53−523+523−52−1−5−1+53+52-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+52-1-1-1-10000220000−1+52−1+52−1−52−1−520000−1+52−1+52−1−52−1−5200000000
χ22444443−52−1−5−1+53+523−523+52−1−5−1+5−1−5−1+53−523+523−52−1−5−1+53+52-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+52-1-1-1-10000-2-200001−521−521+521+5200001−521−521+521+5200000000
χ23444443+52−1+5−1−53−523+523−52−1+5−1−5−1+5−1−53+523−523+52−1+5−1−53−52-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−52-1-1-1-10000220000−1−52−1−52−1+52−1+520000−1−52−1−52−1+52−1+5200000000
χ24444443+52−1+5−1−53−523+523−52−1+5−1−5−1+5−1−53+523−523+52−1+5−1−53−52-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−52-1-1-1-10000-2-200001+521+521−521−5200001+521+521−521−5200000000
χ2544444−1−53+523−52−1+5−1−5−1+53+523−523+523−52−1−5−1+5−1−53+523−52−1+5-1-1-1-1−1−5−1−53+523+523−523−52−1+5−1+5-1-1-1-1222200−1−52−1+52−1−52−1+520000−1−52−1+52−1−52−1+52000000000000
χ2644444−1−53+523−52−1+5−1−5−1+53+523−523+523−52−1−5−1+5−1−53+523−52−1+5-1-1-1-1−1−5−1−53+523+523−523−52−1+5−1+5-1-1-1-1-2-2-2-2001+521−521+521−5200001+521−521+521−52000000000000
χ274444-4−1+53−523+52−1−5−1+5−1−53−523+523−523+52−1+5−1−5−1+53−523+52−1−5-1-1-1-11−51−5−3+52−3+52−3−52−3−521+51+5111122-2-2001−521+521−521+520000−1+52−1−52−1+52−1−52000000000000
χ284444-4−1+53−523+52−1−5−1+5−1−53−523+523−523+52−1+5−1−5−1+53−523+52−1−5-1-1-1-11−51−5−3+52−3+52−3−52−3−521+51+51111-2-22200−1+52−1−52−1+52−1−5200001−521+521−521+52000000000000
χ294444-43−52−1−5−1+53+523−523+52−1−5−1+5−1−5−1+53−523+523−52−1−5−1+53+52-1-1-1-1−3+52−3+521+51+51−51−5−3−52−3−52111100002-200001−521−521+521+520000−1+52−1+52−1−52−1−5200000000
χ304444-43−52−1−5−1+53+523−523+52−1−5−1+5−1−5−1+53−523+523−52−1−5−1+53+52-1-1-1-1−3+52−3+521+51+51−51−5−3−52−3−5211110000-220000−1+52−1+52−1−52−1−5200001−521−521+521+5200000000
χ314444-43+52−1+5−1−53−523+523−52−1+5−1−5−1+5−1−53+523−523+52−1+5−1−53−52-1-1-1-1−3−52−3−521−51−51+51+5−3+52−3+52111100002-200001+521+521−521−520000−1−52−1−52−1+52−1+5200000000
χ324444-43+52−1+5−1−53−523+523−52−1+5−1−5−1+5−1−53+523−523+52−1+5−1−53−52-1-1-1-1−3−52−3−521−51−51+51+5−3+52−3+5211110000-220000−1−52−1−52−1+52−1+5200001+521+521−521−5200000000
χ334444-4−1−53+523−52−1+5−1−5−1+53+523−523+523−52−1−5−1+5−1−53+523−52−1+5-1-1-1-11+51+5−3−52−3−52−3+52−3+521−51−5111122-2-2001+521−521+521−520000−1−52−1+52−1−52−1+52000000000000
χ344444-4−1−53+523−52−1+5−1−5−1+53+523−523+523−52−1−5−1+5−1−53+523−52−1+5-1-1-1-11+51+5−3−52−3−52−3+52−3+521−51−51111-2-22200−1−52−1+52−1−52−1+5200001+521−521+521−52000000000000
χ354-44-40−1+53−523+52−1−5−1+5−1−5−3+52−3−523−523+521−51+51−5−3+52−3−521+5-1-111003ζ6+3ζ14+2ζ22+2ζ38−3ζ6−3ζ14−2ζ22−2ζ38−2ζ6−2ζ14−3ζ22−3ζ382ζ6+2ζ14+3ζ22+3ζ3800i5i5−i5−i52i−2i2-200−1+52−1−521−521+520000−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14000000000000
χ364-44-40−1+53−523+52−1−5−1+5−1−5−3+52−3−523−523+521−51+51−5−3+52−3−521+5-1-111003ζ6+3ζ14+2ζ22+2ζ38−3ζ6−3ζ14−2ζ22−2ζ38−2ζ6−2ζ14−3ζ22−3ζ382ζ6+2ζ14+3ζ22+3ζ3800i5i5−i5−i5−2i2i-22001−521+52−1+52−1−520000ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14000000000000
χ374-44-40−1+53−523+52−1−5−1+5−1−5−3+52−3−523−523+521−51+51−5−3+52−3−521+5-1-11100−3ζ6−3ζ14−2ζ22−2ζ383ζ6+3ζ14+2ζ22+2ζ382ζ6+2ζ14+3ζ22+3ζ38−2ζ6−2ζ14−3ζ22−3ζ3800−i5−i5i5i52i−2i-22001−521+52−1+52−1−520000−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14000000000000
χ384-44-40−1+53−523+52−1−5−1+5−1−5−3+52−3−523−523+521−51+51−5−3+52−3−521+5-1-11100−3ζ6−3ζ14−2ζ22−2ζ383ζ6+3ζ14+2ζ22+2ζ382ζ6+2ζ14+3ζ22+3ζ38−2ζ6−2ζ14−3ζ22−3ζ3800−i5−i5i5i5−2i2i2-200−1+52−1−521−521+520000ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14000000000000
χ394-44-40−1−53+523−52−1+5−1−5−1+5−3−52−3+523+523−521+51−51+5−3−52−3+521−5-1-11100−2ζ6−2ζ14−3ζ22−3ζ382ζ6+2ζ14+3ζ22+3ζ383ζ6+3ζ14+2ζ22+2ζ38−3ζ6−3ζ14−2ζ22−2ζ3800i5i5−i5−i52i−2i-22001+521−52−1−52−1+520000−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38000000000000
χ404-44-40−1−53+523−52−1+5−1−5−1+5−3−52−3+523+523−521+51−51+5−3−52−3+521−5-1-11100−2ζ6−2ζ14−3ζ22−3ζ382ζ6+2ζ14+3ζ22+3ζ383ζ6+3ζ14+2ζ22+2ζ38−3ζ6−3ζ14−2ζ22−2ζ3800i5i5−i5−i5−2i2i2-200−1−52−1+521+521−520000ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38000000000000
χ414-44-40−1−53+523−52−1+5−1−5−1+5−3−52−3+523+523−521+51−51+5−3−52−3+521−5-1-111002ζ6+2ζ14+3ζ22+3ζ38−2ζ6−2ζ14−3ζ22−3ζ38−3ζ6−3ζ14−2ζ22−2ζ383ζ6+3ζ14+2ζ22+2ζ3800−i5−i5i5i52i−2i2-200−1−52−1+521+521−520000−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38000000000000
χ424-44-40−1−53+523−52−1+5−1−5−1+5−3−52−3+523+523−521+51−51+5−3−52−3+521−5-1-111002ζ6+2ζ14+3ζ22+3ζ38−2ζ6−2ζ14−3ζ22−3ζ38−3ζ6−3ζ14−2ζ22−2ζ383ζ6+3ζ14+2ζ22+2ζ3800−i5−i5i5i5−2i2i-22001+521−52−1−52−1+520000ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38000000000000
χ434-4-4404444-4-444-4-444-4-4-4-44-44-4000000000000000000000000000000000000000000
χ444-4-4403−52−1−5−1+53+52−3+52−3−52−1−5−1+51+51−53−523+52−3+521+51−5−3−52-11-113ζ6+3ζ14+2ζ22+2ζ38−3ζ6−3ζ14−2ζ22−2ζ380000−2ζ6−2ζ14−3ζ22−3ζ382ζ6+2ζ14+3ζ22+3ζ38i5−i5i5−i50000000000ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ1400000000
χ454-4-4403−52−1−5−1+53+52−3+52−3−52−1−5−1+51+51−53−523+52−3+521+51−5−3−52-11-113ζ6+3ζ14+2ζ22+2ζ38−3ζ6−3ζ14−2ζ22−2ζ380000−2ζ6−2ζ14−3ζ22−3ζ382ζ6+2ζ14+3ζ22+3ζ38i5−i5i5−i50000000000−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ1400000000
χ464-4-4403−52−1−5−1+53+52−3+52−3−52−1−5−1+51+51−53−523+52−3+521+51−5−3−52-11-11−3ζ6−3ζ14−2ζ22−2ζ383ζ6+3ζ14+2ζ22+2ζ3800002ζ6+2ζ14+3ζ22+3ζ38−2ζ6−2ζ14−3ζ22−3ζ38−i5i5−i5i50000000000ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000ζ22−ζ38−ζ22+ζ38−ζ6+ζ14ζ6−ζ1400000000
χ474-4-4403−52−1−5−1+53+52−3+52−3−52−1−5−1+51+51−53−523+52−3+521+51−5−3−52-11-11−3ζ6−3ζ14−2ζ22−2ζ383ζ6+3ζ14+2ζ22+2ζ3800002ζ6+2ζ14+3ζ22+3ζ38−2ζ6−2ζ14−3ζ22−3ζ38−i5i5−i5i50000000000−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000−ζ22+ζ38ζ22−ζ38ζ6−ζ14−ζ6+ζ1400000000
χ484-4-4403+52−1+5−1−53−52−3−52−3+52−1+5−1−51−51+53+523−52−3−521−51+5−3+52-11-11−2ζ6−2ζ14−3ζ22−3ζ382ζ6+2ζ14+3ζ22+3ζ3800003ζ6+3ζ14+2ζ22+2ζ38−3ζ6−3ζ14−2ζ22−2ζ38i5−i5i5−i50000000000−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ3800000000
χ494-4-4403+52−1+5−1−53−52−3−52−3+52−1+5−1−51−51+53+523−52−3−521−51+5−3+52-11-11−2ζ6−2ζ14−3ζ22−3ζ382ζ6+2ζ14+3ζ22+3ζ3800003ζ6+3ζ14+2ζ22+2ζ38−3ζ6−3ζ14−2ζ22−2ζ38i5−i5i5−i50000000000ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ3800000000
χ504-4-4403+52−1+5−1−53−52−3−52−3+52−1+5−1−51−51+53+523−52−3−521−51+5−3+52-11-112ζ6+2ζ14+3ζ22+3ζ38−2ζ6−2ζ14−3ζ22−3ζ380000−3ζ6−3ζ14−2ζ22−2ζ383ζ6+3ζ14+2ζ22+2ζ38−i5i5−i5i50000000000−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000−ζ6+ζ14ζ6−ζ14−ζ22+ζ38ζ22−ζ3800000000
χ514-4-4403+52−1+5−1−53−52−3−52−3+52−1+5−1−51−51+53+523−52−3−521−51+5−3+52-11-112ζ6+2ζ14+3ζ22+3ζ38−2ζ6−2ζ14−3ζ22−3ζ380000−3ζ6−3ζ14−2ζ22−2ζ383ζ6+3ζ14+2ζ22+2ζ38−i5i5−i5i50000000000ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000ζ6−ζ14−ζ6+ζ14ζ22−ζ38−ζ22+ζ3800000000
χ5288888-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-23333-2-2-2-2-2-2-2-23333000000000000000000000000000000
χ538888-8-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2333322222222-3-3-3-3000000000000000000000000000000
χ5488-8-80-2-2-2-222222222-2-2-2-23-3-33000000005-5-55000000000000000000000000000000
χ5588-8-80-2-2-2-222222222-2-2-2-23-3-3300000000-555-5000000000000000000000000000000
χ5688-8-80−2+253−53+5−2−252−252+25−3+5−3−5−3+5−3−52−252+25−2+253−53+5−2−25-222-2000000000000000000000000000000000000000000
χ5788-8-803−5−2−25−2+253+5−3+5−3−52+252−252+252−25−3+5−3−53−5−2−25−2+253+5-222-2000000000000000000000000000000000000000000
χ5888-8-803+5−2+25−2−253−5−3−5−3+52−252+252−252+25−3−5−3+53+5−2+25−2−253−5-222-2000000000000000000000000000000000000000000
χ5988-8-80−2−253+53−5−2+252+252−25−3−5−3+5−3−5−3+52+252−25−2−253+53−5−2+25-222-2000000000000000000000000000000000000000000
χ608-88-80-2-2-2-2-2-222-2-222222233-3-3002i5−2i52i5−2i500−i5−i5i5i5000000000000000000000000000000
χ618-88-80-2-2-2-2-2-222-2-222222233-3-300−2i52i5−2i52i500i5i5−i5−i5000000000000000000000000000000
χ628-88-803−5−2−25−2+253+53−53+52+252−25−2−25−2+25−3+5−3−5−3+52+252−25−3−5-2-222000000000000000000000000000000000000000000
χ638-88-803+5−2+25−2−253−53+53−52−252+25−2+25−2−25−3−5−3+5−3−52−252+25−3+5-2-222000000000000000000000000000000000000000000
χ648-8-880-2-2-2-222-2-222-2-222223-33-32i5−2i500002i5−2i5−i5i5−i5i5000000000000000000000000000000
χ658-8-880-2-2-2-222-2-222-2-222223-33-3−2i52i50000−2i52i5i5−i5i5−i5000000000000000000000000000000
χ668-8-880−2+253−53+5−2−252−252+253−53+5−3+5−3−5−2+25−2−252−25−3+5−3−52+25-22-22000000000000000000000000000000000000000000
χ678-8-880−2−253+53−5−2+252+252−253+53−5−3−5−3+5−2−25−2+252+25−3−5−3+52−25-22-22000000000000000000000000000000000000000000

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