Finite Group Databasebeta

← Group #14513379

Character table — Group #14513379

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222444466668888101010101212121212121212121212121212121216161616161616161616161616161616161624242424242424242424242424242424303030303030303060606060606080808080
order12442455101020202020101020202244361212888822448888101010102020202061215153030303030306060606060606060101010102020202040404040404040404444888844888824242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ311111111111111111111111111-1-1-1-111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ51111-1-111111111-1-1-1-1-11-11111111-1-11-11-111-1-111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-1
χ61111-1-111111111-1-1-1-1-11-11111111-1-1-11-11-1-11111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1
χ71111-1-111111111-1-1-1-1-11-111111-1-1111-11-111-1-111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ81111-1-111111111-1-1-1-1-11-111111-1-111-11-11-1-11111-1-1-1-111-1-111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-111-1-111-1-1-1-111
χ911-1-11-11111-1-1-1-111-1-1-1-11111-1-1i−ii−i1-1-111-11-1-1-1-1-111111-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1ii−i−ii−ii−ii−ii−ii−ii−ii−i
χ1011-1-11-11111-1-1-1-111-1-1-1-11111-1-1i−ii−i-111-1-11-11-1-1-1-111111-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−iiii−ii−i−ii−ii−iii−ii−i
χ1111-1-11-11111-1-1-1-111-1-1-1-11111-1-1−ii−ii1-1-111-11-1-1-1-1-111111-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1−i−iii−ii−ii−ii−ii−ii−ii−ii
χ1211-1-11-11111-1-1-1-111-1-1-1-11111-1-1−ii−ii-111-1-11-11-1-1-1-111111-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111ii−i−i−ii−iii−ii−ii−i−ii−ii
χ1311-1-1-111111-1-1-1-1-1-1111-1-1111-1-1i−i−ii11-1-11-1-11-1-111-1-111-1111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111ii−i−ii−i−ii−iii−i−iii−i−ii
χ1411-1-1-111111-1-1-1-1-1-1111-1-1111-1-1i−i−ii-1-111-111-1-1-111-1-111-1111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1−i−iiii−i−iii−i−iii−ii−i−ii
χ1511-1-1-111111-1-1-1-1-1-1111-1-1111-1-1−iii−i11-1-11-1-11-1-111-1-111-1111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111−i−iii−iii−ii−i−iii−i−iii−i
χ1611-1-1-111111-1-1-1-1-1-1111-1-1111-1-1−iii−i-1-111-111-1-1-111-1-111-1111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1ii−i−i−iii−i−iii−i−ii−iii−i
χ172222222222222222222222-1-1-1-122220000000022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000002222000000-1-1-1-1
χ182222222222222222222222-1-1-1-1-2-2-2-20000000022222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000-2-2-2-20000001111
χ19222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+5222222222000022222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52000000000000000000
χ20222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52222222220000-2-2-2-2-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−521+521−521+521−521+521−521+521−521+521−521+521−521+521−52000000000000000000
χ21222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−5222222222000022222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52000000000000000000
χ22222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52222222220000-2-2-2-2-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+521−521+521−521+521−521+521−521+521−521+521−521+52000000000000000000
χ232222-2-222222222-2-2-2-2-22-22-1-1-1-122-2-20000000022-2-2-2-22211-1-11111-1-1-1-1-1-111110000000000000000000022-2-2000000-1-111
χ242222-2-222222222-2-2-2-2-22-22-1-1-1-1-2-2220000000022-2-2-2-22211-1-11111-1-1-1-1-1-1111100000000000000000000-2-22200000011-1-1
χ252222-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521−521+521−52-22-22222200002-22-222-2-2−1−52−1+521+521−521+521−52−1−52−1+52-2-2−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1+52−1−52−1+521+521−521+521−52000000000000000000
χ262222-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521−521+521−52-22-2222220000-22-22-2-222−1−52−1+521+521−521+521−52−1−52−1+52-2-2−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521−52−1−52−1+521+521−52−1−52−1+521+521−521+521−52−1−52−1+52−1−52−1+52000000000000000000
χ272222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521+521−521+52-22-22222200002-22-222-2-2−1+52−1−521−521+521−521+52−1+52−1−52-2-2−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1−52−1+52−1−521−521+521−521+52000000000000000000
χ282222-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521+521−521+52-22-2222220000-22-22-2-222−1+52−1−521−521+521−521+52−1+52−1−52-2-2−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521+52−1+52−1−521−521+52−1+52−1−521−521+521−521+52−1+52−1−52−1+52−1−52000000000000000000
χ2922-2-22-22222-2-2-2-222-2-2-2-222-1-1112i−2i2i−2i00000000-2-2-2-22222-11-1-1-1-1-1-1-1-111111111000000000000000000002i−2i2i−2i000000−ii−ii
χ3022-2-22-22222-2-2-2-222-2-2-2-222-1-111−2i2i−2i2i00000000-2-2-2-22222-11-1-1-1-1-1-1-1-11111111100000000000000000000−2i2i−2i2i000000i−ii−i
χ3122-2-22-2−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1+521+521−52-2-22222-2-200002-2-222-22-21+521−521+521−52−1−52−1+52−1−52−1+522-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+521+521−521+521−52−1−52−1+52−1−52−1+521+521−52−1−52−1+521+521−52000000000000000000
χ3222-2-22-2−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1+521+521−52-2-22222-2-20000-222-2-22-221+521−521+521−52−1−52−1+52−1−52−1+522-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521−52−1−52−1+52−1−52−1+521+521−521+521−52−1−52−1+521+521−52−1−52−1+52000000000000000000
χ3322-2-22-2−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1−521−521+52-2-22222-2-200002-2-222-22-21−521+521−521+52−1+52−1−52−1+52−1−522-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−521−521+521−521+52−1+52−1−52−1+52−1−521−521+52−1+52−1−521−521+52000000000000000000
χ3422-2-22-2−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1−521−521+52-2-22222-2-20000-222-2-22-221−521+521−521+52−1+52−1−52−1+52−1−522-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521+52−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1−521−521+52−1+52−1−52000000000000000000
χ3522-2-2-222222-2-2-2-2-2-2222-2-22-1-1112i−2i−2i2i00000000-2-222-2-2221-1-1-11111-1-11111-1-1-1-1000000000000000000002i−2i−2i2i000000−iii−i
χ3622-2-2-222222-2-2-2-2-2-2222-2-22-1-111−2i2i2i−2i00000000-2-222-2-2221-1-1-11111-1-11111-1-1-1-100000000000000000000−2i2i2i−2i000000i−i−ii
χ3722-2-2-22−1−52−1+52−1−52−1+521+521+521−521−521+521−52−1−52−1+522-2-2222-2-2000022-2-22-2-221+521−52−1−52−1+521+521−52−1−52−1+52-22−1−52−1+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+521+521−521+521−52−1−52−1+521+521−521+521−52−1−52−1+52000000000000000000
χ3822-2-2-22−1−52−1+52−1−52−1+521+521+521−521−521+521−52−1−52−1+522-2-2222-2-20000-2-222-222-21+521−52−1−52−1+521+521−52−1−52−1+52-22−1−52−1+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521−521+521−52−1−52−1+52−1−52−1+521+521−52−1−52−1+52−1−52−1+521+521−52000000000000000000
χ3922-2-2-22−1+52−1−52−1+52−1−521−521−521+521+521−521+52−1+52−1−522-2-2222-2-2000022-2-22-2-221−521+52−1+52−1−521−521+52−1+52−1−52-22−1+52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1−521−521+521−521+52−1+52−1−52000000000000000000
χ4022-2-2-22−1+52−1−52−1+52−1−521−521−521+521+521−521+52−1+52−1−522-2-2222-2-20000-2-222-222-21−521+52−1+52−1−521−521+52−1+52−1−52-22−1+52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521+521−521+52−1+52−1−52−1+52−1−521−521+52−1+52−1−52−1+52−1−521−521+52000000000000000000
χ41333333333333333333-1-1-1-1000033331111-1-1-1-1-1-1-1-1-1-1-1-100000000000000000011111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111110000
χ42333333333333333333-1-1-1-100003333-1-1-1-11111-1-1-1-1-1-1-1-1000000000000000000-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-10000
χ43333333333333333333-1-1-1-10000-3-3-3-31111-1-1-1-1-1-1-1-1-1-1-1-100000000000000000011111111-1-1-1-1-1-1-1-11111111111-1-1-1-10000
χ44333333333333333333-1-1-1-10000-3-3-3-3-1-1-1-11111-1-1-1-1-1-1-1-1000000000000000000-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111110000
χ453333-3-333333333-3-3-3-31-11-1000033-3-31-11-1-1-111-1-11111-1-100000000000000000011-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-10000
χ463333-3-333333333-3-3-3-31-11-1000033-3-3-11-1111-1-1-1-11111-1-1000000000000000000-1-111-1-1111111-1-1-1-11111-1-111-1-1-1-1110000
χ473333-3-333333333-3-3-3-31-11-10000-3-3331-11-1-1-111-1-11111-1-100000000000000000011-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1110000
χ483333-3-333333333-3-3-3-31-11-10000-3-333-11-1111-1-1-1-11111-1-1000000000000000000-1-111-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-10000
χ4933-3-33-33333-3-3-3-333-3-311-1-100003i−3i3i−3i1-1-11-11-111111-1-1-1-100000000000000000011-1-1-1-111-1-111-1-111−i−iii−ii−ii−iii−ii−i0000
χ5033-3-33-33333-3-3-3-333-3-311-1-100003i−3i3i−3i-111-11-11-11111-1-1-1-1000000000000000000-1-11111-1-111-1-111-1-1ii−i−i−ii−iii−i−ii−ii0000
χ5133-3-33-33333-3-3-3-333-3-311-1-10000−3i3i−3i3i1-1-11-11-111111-1-1-1-100000000000000000011-1-1-1-111-1-111-1-111ii−i−ii−ii−ii−i−ii−ii0000
χ5233-3-33-33333-3-3-3-333-3-311-1-10000−3i3i−3i3i-111-11-11-11111-1-1-1-1000000000000000000-1-11111-1-111-1-111-1-1−i−iiii−ii−i−iii−ii−i0000
χ5333-3-3-333333-3-3-3-3-3-333-111-100003i−3i−3i3i11-1-1-111-111-1-111-1-10000000000000000001111-1-1-1-1-1-11111-1-1−i−iii−iii−ii−ii−i−ii0000
χ5433-3-3-333333-3-3-3-3-3-333-111-100003i−3i−3i3i-1-1111-1-1111-1-111-1-1000000000000000000-1-1-1-1111111-1-1-1-111ii−i−i−iii−i−ii−iii−i0000
χ5533-3-3-333333-3-3-3-3-3-333-111-10000−3i3i3i−3i11-1-1-111-111-1-111-1-10000000000000000001111-1-1-1-1-1-11111-1-1ii−i−ii−i−ii−ii−iii−i0000
χ5633-3-3-333333-3-3-3-3-3-333-111-10000−3i3i3i−3i-1-1111-1-1111-1-111-1-1000000000000000000-1-1-1-1111111-1-1-1-111−i−iiii−i−iii−ii−i−ii0000
χ57444444−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5−1−5−1+54444-2-2-2-2000000000000−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-2-21+521−521+521+521−521−521+521−521+521+521−521−521+521+521−521−520000000000000000000000000000000000
χ58444444−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5−1+5−1−54444-2-2-2-2000000000000−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-2-21−521+521−521−521+521+521−521+521−521−521+521+521−521−521+521+520000000000000000000000000000000000
χ594444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+51+51−51+51−5-44-44-2-2-2-2000000000000−1−5−1+51+51−51+51−5−1−5−1+5221+521−52−1−52−1−52−1+52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+520000000000000000000000000000000000
χ604444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−51−51+51−51+5-44-44-2-2-2-2000000000000−1+5−1−51−51+51−51+5−1+5−1−5221−521+52−1+52−1+52−1−52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−520000000000000000000000000000000000
χ6144-4-44-4−1−5−1+5−1−5−1+51+51+51−51−5−1−5−1+51+51−5-4-444-2-2220000000000001+51−51+51−5−1−5−1+5−1−5−1+5-221+521−521+521+521−521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000000000000000000000000000
χ6244-4-44-4−1+5−1−5−1+5−1−51−51−51+51+5−1+5−1−51−51+5-4-444-2-2220000000000001−51+51−51+5−1+5−1−5−1+5−1−5-221−521+521−521−521+521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000000000000000000000000000
χ6344-4-4-44−1−5−1+5−1−5−1+51+51+51−51−51+51−5−1−5−1+54-4-44-2-2220000000000001+51−5−1−5−1+51+51−5−1−5−1+52-21+521−52−1−52−1−52−1+52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−520000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.