Finite Group Databasebeta

← Group #85596

Character table — Group #85596

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size1111222222444444446688888888888812121211112222224444444466888888888888121212
order1222444444336666664412121212121212121212121222422224444446666666644121212121212121212121212224
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32111
χ31111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32111
χ4111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11
χ5111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-11111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-11
χ6111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-11111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-11
χ71111-1-111-1-11111111111-1-1-1-111-1-111-1-11-1-11111-1-111-1-11111111111-1-1-1-111-1-111-1-11-1-1
χ81111-1-111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1-11111-1-111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1-1
χ91111-1-111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1-11111-1-111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1-1
χ101111-1-1-1-1111111111111-1-1-1-1-1-111-1-111-11-11111-1-1-1-1111111111111-1-1-1-1-1-111-1-111-11-1
χ111111-1-1-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-11-11111-1-1-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-11-1
χ121111-1-1-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-11-11111-1-1-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-11-1
χ1322-2-22-22i−2i2i−2i-1-111-1-111001-11-1i−ii−ii−ii−i00022-2-22-22i−2i2i−2i-1-111-1-111001-11-1i−ii−ii−ii−i000
χ1422-2-22-22i−2i2i−2i1+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i3200−1−i321+i32−1+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ700022-2-22-22i−2i2i−2i1+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i3200−1−i321+i32−1+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7000
χ1522-2-22-22i−2i2i−2i1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i3200−1+i321−i32−1−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ1100022-2-22-22i−2i2i−2i1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i3200−1+i321−i32−1−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11000
χ1622-2-22-2−2i2i−2i2i-1-111-1-111001-11-1−ii−ii−ii−ii00022-2-22-2−2i2i−2i2i-1-111-1-111001-11-1−ii−ii−ii−ii000
χ1722-2-22-2−2i2i−2i2i1+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i3200−1−i321+i32−1+i321−i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ700022-2-22-2−2i2i−2i2i1+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i3200−1−i321+i32−1+i321−i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7000
χ1822-2-22-2−2i2i−2i2i1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i3200−1+i321−i32−1−i321+i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ1100022-2-22-2−2i2i−2i2i1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i3200−1+i321−i32−1−i321+i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11000
χ1922-2-2-222i−2i−2i2i-1-111-1-11100-11-11i−i−iii−i−ii00022-2-2-222i−2i−2i2i-1-111-1-11100-11-11i−i−iii−i−ii000
χ2022-2-2-222i−2i−2i2i1+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32001+i32−1−i321−i32−1+i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ700022-2-2-222i−2i−2i2i1+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32001+i32−1−i321−i32−1+i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7000
χ2122-2-2-222i−2i−2i2i1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32001−i32−1+i321+i32−1−i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ1100022-2-2-222i−2i−2i2i1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32001−i32−1+i321+i32−1−i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11000
χ2222-2-2-22−2i2i2i−2i-1-111-1-11100-11-11−iii−i−iii−i00022-2-2-22−2i2i2i−2i-1-111-1-11100-11-11−iii−i−iii−i000
χ2322-2-2-22−2i2i2i−2i1+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32001+i32−1−i321−i32−1+i32−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ700022-2-2-22−2i2i2i−2i1+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32001+i32−1−i321−i32−1+i32−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7000
χ2422-2-2-22−2i2i2i−2i1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32001−i32−1+i321+i32−1−i32−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ1100022-2-2-22−2i2i2i−2i1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32001−i32−1+i321+i32−1−i32−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11000
χ252-2-2200000022-2-2-2-2222-20000000000000002-2-2200000022-2-2-2-2222-2000000000000000
χ262-2-22000000−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i32-20000000000000002-2-22000000−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i32-2000000000000000
χ272-2-22000000−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i32-20000000000000002-2-22000000−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i32-2000000000000000
χ28333333333300000000-1-1000000000000-1-1-1333333333300000000-1-1000000000000-1-1-1
χ29333333-3-3-3-300000000-1-100000000000011-1333333-3-3-3-300000000-1-100000000000011-1
χ303333-3-333-3-300000000-1-1000000000000-1113333-3-333-3-300000000-1-1000000000000-111
χ313333-3-3-3-33300000000-1-10000000000001-113333-3-3-3-33300000000-1-10000000000001-11
χ324-44-4000000-2-2-2-22222000000000000000004-44-4000000-2-2-2-2222200000000000000000
χ334-44-40000001+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i3000000000000000004-44-40000001+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i300000000000000000
χ344-44-40000001−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i3000000000000000004-44-40000001−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i300000000000000000
χ356-6-6600000000000000-220000000000000006-6-6600000000000000-22000000000000000
χ3611111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ371111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32111-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1-11+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1
χ381111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32111-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1-11−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1
χ39111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1
χ40111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-11-1-1-1-1-1-111111+i321−i321+i321−i321+i321−i321+i321−i32-1-11+i321+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211-1
χ41111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-11-1-1-1-1-1-111111−i321+i321−i321+i321−i321+i321−i321+i32-1-11−i321−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211-1
χ421111-1-111-1-11111111111-1-1-1-111-1-111-1-11-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-111
χ431111-1-111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1-1-1-1-1-111-1-1111+i321−i321+i321−i321+i321−i321+i321−i32-1-1−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-111
χ441111-1-111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1-1-1-1-1-111-1-1111−i321+i321−i321+i321−i321+i321−i321+i32-1-1−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-111
χ451111-1-1-1-1111111111111-1-1-1-1-1-111-1-111-11-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11-11
χ461111-1-1-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-11-1-1-1-1-11111-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-11
χ471111-1-1-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-11-1-1-1-1-11111-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-11
χ4822-2-22-22i−2i2i−2i-1-111-1-111001-11-1i−ii−ii−ii−i000-2-222-22−2i2i−2i2i11-1-111-1-100-11-11−ii−ii−ii−ii000
χ4922-2-22-22i−2i2i−2i1+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i3200−1−i321+i32−1+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7000-2-222-22−2i2i−2i2i−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32001+i32−1−i321−i32−1+i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7000
χ5022-2-22-22i−2i2i−2i1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i3200−1+i321−i32−1−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11000-2-222-22−2i2i−2i2i−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32001−i32−1+i321+i32−1−i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11000
χ5122-2-22-2−2i2i−2i2i-1-111-1-111001-11-1−ii−ii−ii−ii000-2-222-222i−2i2i−2i11-1-111-1-100-11-11i−ii−ii−ii−i000
χ5222-2-22-2−2i2i−2i2i1+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i3200−1−i321+i32−1+i321−i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7000-2-222-222i−2i2i−2i−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32001+i32−1−i321−i32−1+i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7000
χ5322-2-22-2−2i2i−2i2i1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i3200−1+i321−i32−1−i321+i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11000-2-222-222i−2i2i−2i−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32001−i32−1+i321+i32−1−i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11000
χ5422-2-2-222i−2i−2i2i-1-111-1-11100-11-11i−i−iii−i−ii000-2-2222-2−2i2i2i−2i11-1-111-1-1001-11-1−iii−i−iii−i000
χ5522-2-2-222i−2i−2i2i1+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32001+i32−1−i321−i32−1+i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7000-2-2222-2−2i2i2i−2i−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i3200−1−i321+i32−1+i321−i32−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7000
χ5622-2-2-222i−2i−2i2i1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32001−i32−1+i321+i32−1−i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11000-2-2222-2−2i2i2i−2i−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i3200−1+i321−i32−1−i321+i32−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11000
χ5722-2-2-22−2i2i2i−2i-1-111-1-11100-11-11−iii−i−iii−i000-2-2222-22i−2i−2i2i11-1-111-1-1001-11-1i−i−iii−i−ii000
χ5822-2-2-22−2i2i2i−2i1+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32001+i32−1−i321−i32−1+i32−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7000-2-2222-22i−2i−2i2i−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i3200−1−i321+i32−1+i321−i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7000
χ5922-2-2-22−2i2i2i−2i1−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32001−i32−1+i321+i32−1−i32−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11000-2-2222-22i−2i−2i2i−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i3200−1+i321−i32−1−i321+i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11000
χ602-2-2200000022-2-2-2-2222-2000000000000000-222-2000000-2-22222-2-2-22000000000000000
χ612-2-22000000−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i32-2000000000000000-222-20000001+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i3-22000000000000000
χ622-2-22000000−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i32-2000000000000000-222-20000001−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i3-22000000000000000
χ63333333333300000000-1-1000000000000-1-1-1-3-3-3-3-3-3-3-3-3-30000000011000000000000111
χ64333333-3-3-3-300000000-1-100000000000011-1-3-3-3-3-3-333330000000011000000000000-1-11
χ653333-3-333-3-300000000-1-1000000000000-111-3-3-3-333-3-33300000000110000000000001-1-1
χ663333-3-3-3-33300000000-1-10000000000001-11-3-3-3-33333-3-30000000011000000000000-11-1
χ674-44-4000000-2-2-2-2222200000000000000000-44-440000002222-2-2-2-200000000000000000
χ684-44-40000001+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i300000000000000000-44-44000000−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i300000000000000000
χ694-44-40000001−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i300000000000000000-44-44000000−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i300000000000000000
χ706-6-6600000000000000-22000000000000000-666-6000000000000002-2000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.