Finite Group Databasebeta

← Group #68424

Character table — Group #68424

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51
size11112222222244444444466666688888888888881212121212161624242424
order122234444666488881212121222444444881224242424242424244888812124488
χ1111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1-1-11111111111111-1-1-1-1-111-1-1-1-1
χ4111111111111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-1-1-1111111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-11111-1-1
χ61111111111111-1-1-1-11111111111-1-1111-1-1-1-111111-1-1-1-1-1-1-1-111
χ71111111111111-1-1-1-11111-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1111111-1-111
χ81111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-11111-11111-1-111-1-1
χ911111-1-1-1-11111ii−i−i-1-1-1-11111-1-11-1i−i1ii−i−iii−i−i-1ii−i−i1-11-1i−i
χ1011111-1-1-1-11111ii−i−i-1-1-1-11111-1-1-11−ii1ii−i−i−i−iii-1ii−i−i-11-11−ii
χ1111111-1-1-1-11111ii−i−i-1-1-1-1-1-1-1-1111-1i−i1ii−i−iii−i−i1−i−iii1-1-11−ii
χ1211111-1-1-1-11111ii−i−i-1-1-1-1-1-1-1-111-11−ii1ii−i−i−i−iii1−i−iii-111-1i−i
χ1311111-1-1-1-11111−i−iii-1-1-1-11111-1-11-1−ii1−i−iii−i−iii-1−i−iii1-11-1−ii
χ1411111-1-1-1-11111−i−iii-1-1-1-11111-1-1-11i−i1−i−iiiii−i−i-1−i−iii-11-11i−i
χ1511111-1-1-1-11111−i−iii-1-1-1-1-1-1-1-1111-1−ii1−i−iii−i−iii1ii−i−i1-1-11i−i
χ1611111-1-1-1-11111−i−iii-1-1-1-1-1-1-1-111-11i−i1−i−iiiii−i−i1ii−i−i-111-1−ii
χ17222222-2-22222-200002-22-222-2-2220000-200000000-20000000000
χ18222222-2-22222-200002-22-2-2-222-2-20000-20000000020000000000
χ1922222-222-2222-20000-22-2222-2-2-2-20000-20000000020000000000
χ2022222-222-2222-20000-22-22-2-222220000-200000000-20000000000
χ212222-12222-1-1-122222-1-1-1-10000002222-1-1-1-1-1-1-1-1-100000-1-10000
χ222222-12222-1-1-122222-1-1-1-1000000-2-2-2-2-1-1-1-1-1111100000110000
χ232222-12222-1-1-12-2-2-2-2-1-1-1-100000022-2-2-11111111100000-1-10000
χ242222-12222-1-1-12-2-2-2-2-1-1-1-1000000-2-222-11111-1-1-1-100000110000
χ252222-1-2-2-2-2-1-1-122i2i−2i−2i11110000002-22i−2i-1−i−iii−i−iii00000-110000
χ262222-1-2-2-2-2-1-1-122i2i−2i−2i1111000000-22−2i2i-1−i−iiiii−i−i000001-10000
χ272222-1-2-2-2-2-1-1-12−2i−2i2i2i11110000002-2−2i2i-1ii−i−iii−i−i00000-110000
χ282222-1-2-2-2-2-1-1-12−2i−2i2i2i1111000000-222i−2i-1ii−i−i−i−iii000001-10000
χ292-22-2202-20-2-2202−22−20-202002i−2i2i−2i000002−22−200000−i2i2−i2i2000000
χ302-22-2202-20-2-2202−22−20-20200−2i2i−2i2i000002−22−200000i2−i2i2−i2000000
χ312-22-2202-20-2-220−22−220-202002i−2i2i−2i00000−22−2200000i2−i2i2−i2000000
χ322-22-2202-20-2-220−22−220-20200−2i2i−2i2i00000−22−2200000−i2i2−i2i2000000
χ332-22-220-220-2-220−i2i2i2−i2020-2002i−2i−2i2i00000−i2i2i2−i200000−222−2000000
χ342-22-220-220-2-220−i2i2i2−i2020-200−2i2i2i−2i00000−i2i2i2−i2000002−2−22000000
χ352-22-220-220-2-220i2−i2−i2i2020-2002i−2i−2i2i00000i2−i2−i2i2000002−2−22000000
χ362-22-220-220-2-220i2−i2−i2i2020-200−2i2i2i−2i00000i2−i2−i2i200000−222−2000000
χ374444-24-4-44-2-2-2-40000-22-22000000000020000000000000000000
χ384444-2-444-4-2-2-2-400002-22-2000000000020000000000000000000
χ3944-4-4400004-4-40000000004-40000000000000000000000000000
χ4044-4-4400004-4-4000000000-440000000000000000000000000000
χ414-44-4-204-4022-2022−2222−22020-200000000000−22−22000000000000000
χ424-44-4-204-4022-20−2222−2222020-2000000000002−22−2000000000000000
χ434-44-4-20-44022-20−2i22i22i2−2i20-20200000000000i2−i2−i2i2000000000000000
χ444-44-4-20-44022-202i2−2i2−2i22i20-20200000000000−i2i2i2−i2000000000000000
χ454-4-444400-4-44-40000040-40000000000000000000000000000000
χ464-4-444-4004-44-400000-4040000000000000000000000000000000
χ474-4-44-2400-42-2200000-2020000000000000000i6−i6i6−i600000000000
χ484-4-44-2400-42-2200000-2020000000000000000−i6i6−i6i600000000000
χ494-4-44-2-40042-220000020-200000000000000006−6−6600000000000
χ504-4-44-2-40042-220000020-20000000000000000−666−600000000000
χ5188-8-8-40000-444000000000000000000000000000000000000000

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