Finite Group Databasebeta

← Group #69632

Character table — Group #69632

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111111122222222222222224444444444444488888888888812121212121212121212121212121212
order12222222344444444666666644121212121212121212121212444412121212121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911-1-11-11-11ii−i−i1-11-11-1-11-11-1i−i11-1-1ii−i−iii−i−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i
χ1011-1-11-11-11ii−i−i1-11-11-1-11-11-1i−i11-1-1ii−i−iii−i−i1-1i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii
χ1111-1-11-11-11ii−i−i1-11-11-1-11-11-1i−i11-1-1ii−i−iii−i−i-11−ii-1-111−i−iii11-1-1ii−i−i-1-111−i−iii
χ1211-1-11-11-11ii−i−i1-11-11-1-11-11-1i−i11-1-1ii−i−iii−i−i-11−ii-1-111−i−iii-1-111−i−iii11-1-1ii−i−i
χ1311-1-11-11-11−i−iii1-11-11-1-11-11-1−ii11-1-1−i−iii−i−iii1-1−ii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii
χ1411-1-11-11-11−i−iii1-11-11-1-11-11-1−ii11-1-1−i−iii−i−iii1-1−ii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i
χ1511-1-11-11-11−i−iii1-11-11-1-11-11-1−ii11-1-1−i−iii−i−iii-11i−i-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i
χ1611-1-11-11-11−i−iii1-11-11-1-11-11-1−ii11-1-1−i−iii−i−iii-11i−i-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii
χ172222222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ18222222222-2-2-2-2-2-2-2-2222222222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ1922222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ2022222222-122222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ2122222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-211111111-1-1-1-10000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2222222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-211111111-1-1-1-10000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2322222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-1-1-11111111122-2-2-1-1-1-111110000000000000000
χ2422222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-2-1-1-1-111111111-2-2221111-1-1-1-10000000000000000
χ2522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111-1-1-1-111110000−i3i3−i3i3i3−i3i3−i30000000000000000
χ2622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1221111-1-1-1-111110000i3−i3i3−i3−i3i3−i3i30000000000000000
χ2722-2-22-22-222i2i−2i−2i-22-222-2-22-22-2−2i2i-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ2822-2-22-22-22−2i−2i2i2i-22-222-2-22-22-22i−2i-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ2922-2-22-22-2-12i2i−2i−2i2-22-2-111-11-112i−2i-1-111−i−iii−i−iii2-22i−2i-1-111−i−iii0000000000000000
χ3022-2-22-22-2-12i2i−2i−2i2-22-2-111-11-112i−2i-1-111−i−iii−i−iii-22−2i2i11-1-1ii−i−i0000000000000000
χ3122-2-22-22-2-12i2i−2i−2i-22-22-111-11-11−2i2i11-1-1ii−i−i−i−iii0000−i3i3i3−i33−3−330000000000000000
χ3222-2-22-22-2-12i2i−2i−2i-22-22-111-11-11−2i2i11-1-1ii−i−i−i−iii0000i3−i3−i3i3−333−30000000000000000
χ3322-2-22-22-2-1−2i−2i2i2i2-22-2-111-11-11−2i2i-1-111ii−i−iii−i−i2-2−2i2i-1-111ii−i−i0000000000000000
χ3422-2-22-22-2-1−2i−2i2i2i2-22-2-111-11-11−2i2i-1-111ii−i−iii−i−i-222i−2i11-1-1−i−iii0000000000000000
χ3522-2-22-22-2-1−2i−2i2i2i-22-22-111-11-112i−2i11-1-1−i−iiiii−i−i0000−i3i3i3−i3−333−30000000000000000
χ3622-2-22-22-2-1−2i−2i2i2i-22-22-111-11-112i−2i11-1-1−i−iiiii−i−i0000i3−i3−i3i33−3−330000000000000000
χ372-222-2-22-22000022-2-2-2222-2-2-2002-22-2000000000000000000002-22-2000000000000
χ382-222-2-22-22000022-2-2-2222-2-2-2002-22-200000000000000000000-22-22000000000000
χ392-222-2-22-220000-2-222-2222-2-2-200-22-220000000000000000000000002i−2i2i−2i00000000
χ402-222-2-22-220000-2-222-2222-2-2-200-22-22000000000000000000000000−2i2i−2i2i00000000
χ412-22-222-2-222-22-20000-22-2-2-22200000000002-22-200000000000000000000−i2i2−i2i2−i2i2−i2i2
χ422-22-222-2-222-22-20000-22-2-2-22200000000002-22-200000000000000000000i2−i2i2−i2i2−i2i2−i2
χ432-22-222-2-22-22-220000-22-2-2-2220000000000-22-2200000000000000000000−i2i2−i2i2i2−i2i2−i2
χ442-22-222-2-22-22-220000-22-2-2-2220000000000-22-2200000000000000000000i2−i2i2−i2−i2i2−i2i2
χ452-2-222-2-2222i−2i−2i2i0000-2-22-222-200000000002i−2i−2i2i00000000000000000000−i2i2i2−i22−2−22
χ462-2-222-2-2222i−2i−2i2i0000-2-22-222-200000000002i−2i−2i2i00000000000000000000i2−i2−i2i2−222−2
χ472-2-222-2-222−2i2i2i−2i0000-2-22-222-20000000000−2i2i2i−2i00000000000000000000−i2i2i2−i2−222−2
χ482-2-222-2-222−2i2i2i−2i0000-2-22-222-20000000000−2i2i2i−2i00000000000000000000i2−i2−i2i22−2−22
χ492-2-2-2-2222200002-2-22-2-2-222-22002-2-22000000000000000000002-2-22000000000000
χ502-2-2-2-2222200002-2-22-2-2-222-22002-2-2200000000000000000000-222-2000000000000
χ512-2-2-2-222220000-222-2-2-2-222-2200-222-20000000000000000000000002-2-2200000000
χ522-2-2-2-222220000-222-2-2-2-222-2200-222-2000000000000000000000000-222-200000000
χ53444-4-4-4-4440000000044-4-44-4-4000000000000000000000000000000000000000000
χ54444-4-4-4-44-200000000-2-222-222000000−2i32i3−2i32i300000000000000000000000000000000
χ55444-4-4-4-44-200000000-2-222-2220000002i3−2i32i3−2i300000000000000000000000000000000
χ5644-44-44-4-44000000004-44-4-4-44000000000000000000000000000000000000000000
χ5744-44-44-4-4-200000000-22-2222-200000023−23−232300000000000000000000000000000000
χ5844-44-44-4-4-200000000-22-2222-2000000−232323−2300000000000000000000000000000000
χ594-444-4-44-4-2000044-4-42-2-2-222200-22-22000000000000000000000000000000000000
χ604-444-4-44-4-20000-4-4442-2-2-2222002-22-2000000000000000000000000000000000000
χ614-44-444-4-4-24-44-400002-2222-2-20000000000-22-220000000000000000000000000000
χ624-44-444-4-4-2-44-4400002-2222-2-200000000002-22-20000000000000000000000000000
χ634-4-444-4-44-24i−4i−4i4i000022-22-2-220000000000−2i2i2i−2i0000000000000000000000000000
χ644-4-444-4-44-2−4i4i4i−4i000022-22-2-2200000000002i−2i−2i2i0000000000000000000000000000
χ654-4-4-4-4444-200004-4-44222-2-22-200-222-2000000000000000000000000000000000000
χ664-4-4-4-4444-20000-444-4222-2-22-2002-2-22000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).