Finite Group Databasebeta

← Group #85598

Character table — Group #85598

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size1111222222444444446688888888888812121211112222224444444466888888888888121212
order1222444444336666664412121212121212121212121244422224444446666666644121212121212121212121212444
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
χ4111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-11-1111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-11-1
χ5111111-1-1-1-1−1−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−i32-11-1111111-1-1-1-1−1−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−i32-11-1
χ6111111-1-1-1-1−1+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+i32-11-1111111-1-1-1-1−1+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+i32-11-1
χ71111-1-111-1-11111111111-1-1-1-1-1-111-1-111-1-111111-1-111-1-11111111111-1-1-1-1-1-111-1-111-1-11
χ81111-1-111-1-1−1−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+i32-1-111111-1-111-1-1−1−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+i32-1-11
χ91111-1-111-1-1−1+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−i32-1-111111-1-111-1-1−1+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−i32-1-11
χ101111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-1
χ111111-1-1-1-111−1−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−i321-1-11111-1-1-1-111−1−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−i321-1-1
χ121111-1-1-1-111−1+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+i321-1-11111-1-1-1-111−1+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+i321-1-1
χ1322-2-20000002222-2-2-2-22-200000000000000022-2-20000002222-2-2-2-22-2000000000000000
χ1422-2-2000000−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i32-200000000000000022-2-2000000−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i32-2000000000000000
χ1522-2-2000000−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i32-200000000000000022-2-2000000−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i32-2000000000000000
χ162-2-222i−2i2i−2i2-2-1-111-1-111001-11-1i−ii−ii−ii−i0002-2-222i−2i2i−2i2-2-1-111-1-111001-11-1i−ii−ii−ii−i000
χ172-2-222i−2i2i−2i2-21+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i3200−1−i321+i32−1+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ70002-2-222i−2i2i−2i2-21+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i3200−1−i321+i32−1+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7000
χ182-2-222i−2i2i−2i2-21−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i3200−1+i321−i32−1−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ110002-2-222i−2i2i−2i2-21−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i3200−1+i321−i32−1−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11000
χ192-2-222i−2i−2i2i-22-1-111-1-11100-11-11i−i−iii−i−ii0002-2-222i−2i−2i2i-22-1-111-1-11100-11-11i−i−iii−i−ii000
χ202-2-222i−2i−2i2i-221+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32001+i32−1−i321−i32−1+i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ70002-2-222i−2i−2i2i-221+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32001+i32−1−i321−i32−1+i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7000
χ212-2-222i−2i−2i2i-221−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32001−i32−1+i321+i32−1−i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ110002-2-222i−2i−2i2i-221−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32001−i32−1+i321+i32−1−i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11000
χ222-2-22−2i2i2i−2i-22-1-111-1-11100-11-11−iii−i−iii−i0002-2-22−2i2i2i−2i-22-1-111-1-11100-11-11−iii−i−iii−i000
χ232-2-22−2i2i2i−2i-221+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32001+i32−1−i321−i32−1+i32−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ70002-2-22−2i2i2i−2i-221+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32001+i32−1−i321−i32−1+i32−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7000
χ242-2-22−2i2i2i−2i-221−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32001−i32−1+i321+i32−1−i32−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ110002-2-22−2i2i2i−2i-221−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32001−i32−1+i321+i32−1−i32−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11000
χ252-2-22−2i2i−2i2i2-2-1-111-1-111001-11-1−ii−ii−ii−ii0002-2-22−2i2i−2i2i2-2-1-111-1-111001-11-1−ii−ii−ii−ii000
χ262-2-22−2i2i−2i2i2-21+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i3200−1−i321+i32−1+i321−i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ70002-2-22−2i2i−2i2i2-21+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i3200−1−i321+i32−1+i321−i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7000
χ272-2-22−2i2i−2i2i2-21−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i3200−1+i321−i32−1−i321+i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ110002-2-22−2i2i−2i2i2-21−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i3200−1+i321−i32−1−i321+i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11000
χ28333333333300000000-1-1000000000000-1-1-1333333333300000000-1-1000000000000-1-1-1
χ29333333-3-3-3-300000000-1-10000000000001-11333333-3-3-3-300000000-1-10000000000001-11
χ303333-3-333-3-300000000-1-100000000000011-13333-3-333-3-300000000-1-100000000000011-1
χ313333-3-3-3-33300000000-1-1000000000000-1113333-3-3-3-33300000000-1-1000000000000-111
χ324-44-4000000-2-22222-2-2000000000000000004-44-4000000-2-22222-2-200000000000000000
χ334-44-40000001+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i3000000000000000004-44-40000001+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i300000000000000000
χ344-44-40000001−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i3000000000000000004-44-40000001−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i300000000000000000
χ3566-6-600000000000000-2200000000000000066-6-600000000000000-22000000000000000
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
χ39111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-11-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111-11
χ40111111-1-1-1-1−1−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−i32-11-1-1-1-1-1-1-111111+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+i321-11
χ41111111-1-1-1-1−1+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+i32-11-1-1-1-1-1-1-111111−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−i321-11
χ421111-1-111-1-11111111111-1-1-1-1-1-111-1-111-1-11-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1
χ431111-1-111-1-1−1−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+i32-1-11-1-1-1-111-1-1111+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−i3211-1
χ441111-1-111-1-1−1+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−i32-1-11-1-1-1-111-1-1111−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+i3211-1
χ451111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111
χ461111-1-1-1-111−1−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−i321-1-1-1-1-1-11111-1-11+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+i32-111
χ471111-1-1-1-111−1+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+i321-1-1-1-1-1-11111-1-11−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−i32-111
χ4822-2-20000002222-2-2-2-22-2000000000000000-2-222000000-2-2-2-22222-22000000000000000
χ4922-2-2000000−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i32-2000000000000000-2-2220000001+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i3-22000000000000000
χ5022-2-2000000−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i32-2000000000000000-2-2220000001−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i3-22000000000000000
χ512-2-222i−2i2i−2i2-2-1-111-1-111001-11-1i−ii−ii−ii−i000-222-2−2i2i−2i2i-2211-1-111-1-100-11-11−ii−ii−ii−ii000
χ522-2-222i−2i2i−2i2-21+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i3200−1−i321+i32−1+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7000-222-2−2i2i−2i2i-22−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32001+i32−1−i321−i32−1+i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7000
χ532-2-222i−2i2i−2i2-21−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i3200−1+i321−i32−1−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11000-222-2−2i2i−2i2i-22−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32001−i32−1+i321+i32−1−i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11000
χ542-2-222i−2i−2i2i-22-1-111-1-11100-11-11i−i−iii−i−ii000-222-2−2i2i2i−2i2-211-1-111-1-1001-11-1−iii−i−iii−i000
χ552-2-222i−2i−2i2i-221+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32001+i32−1−i321−i32−1+i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7000-222-2−2i2i2i−2i2-2−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i3200−1−i321+i32−1+i321−i32−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7000
χ562-2-222i−2i−2i2i-221−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32001−i32−1+i321+i32−1−i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11000-222-2−2i2i2i−2i2-2−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i3200−1+i321−i32−1−i321+i32−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11000
χ572-2-22−2i2i2i−2i-22-1-111-1-11100-11-11−iii−i−iii−i000-222-22i−2i−2i2i2-211-1-111-1-1001-11-1i−i−iii−i−ii000
χ582-2-22−2i2i2i−2i-221+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32001+i32−1−i321−i32−1+i32−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7000-222-22i−2i−2i2i2-2−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i3200−1−i321+i32−1+i321−i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7000
χ592-2-22−2i2i2i−2i-221−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32001−i32−1+i321+i32−1−i32−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11000-222-22i−2i−2i2i2-2−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i3200−1+i321−i32−1−i321+i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11000
χ602-2-22−2i2i−2i2i2-2-1-111-1-111001-11-1−ii−ii−ii−ii000-222-22i−2i2i−2i-2211-1-111-1-100-11-11i−ii−ii−ii−i000
χ612-2-22−2i2i−2i2i2-21+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i3200−1−i321+i32−1+i321−i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7000-222-22i−2i2i−2i-22−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32001+i32−1−i321−i32−1+i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7000
χ622-2-22−2i2i−2i2i2-21−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i3200−1+i321−i32−1−i321+i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11000-222-22i−2i2i−2i-22−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32001−i32−1+i321+i32−1−i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11000
χ63333333333300000000-1-1000000000000-1-1-1-3-3-3-3-3-3-3-3-3-30000000011000000000000111
χ64333333-3-3-3-300000000-1-10000000000001-11-3-3-3-3-3-333330000000011000000000000-11-1
χ653333-3-333-3-300000000-1-100000000000011-1-3-3-3-333-3-3330000000011000000000000-1-11
χ663333-3-3-3-33300000000-1-1000000000000-111-3-3-3-33333-3-300000000110000000000001-1-1
χ674-44-4000000-2-22222-2-200000000000000000-44-4400000022-2-2-2-22200000000000000000
χ684-44-40000001+i31−i3−1−i3−1+i3−1−i3−1+i31+i31−i300000000000000000-44-44000000−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i300000000000000000
χ694-44-40000001−i31+i3−1+i3−1−i3−1+i3−1−i31−i31+i300000000000000000-44-44000000−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i300000000000000000
χ7066-6-600000000000000-22000000000000000-6-666000000000000002-2000000000000000

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