Finite Group Databasebeta

← Group #68481

Character table — Group #68481

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size1111222222223333444444444444466668888888888812121212121212121216162424
order122234444666444448888888812121212224444122424242424242424488888888121244
χ1111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111-1-1-1-111111111-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-1111111111111-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1
χ411111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-11111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-1-1
χ6111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-11-1-1-1-11111-11111-1-1-1-1-1-111
χ8111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1-1-1-11111111111-1-1
χ911111-1-1-1-111111111ii−i−iii−i−i-1-1-1-1-1-1-1-11-11ii−i−iii−i−i1ii−i−iii−i−i1-11-1
χ1011111-1-1-1-111111111ii−i−i−i−iii-1-1-1-1-1-1-1-1-111ii−i−i−i−iii1ii−i−i−i−iii-11-11
χ1111111-1-1-1-111111111−i−iiiii−i−i-1-1-1-1-1-1-1-1-111−i−iiiii−i−i1−i−iiiii−i−i-11-11
χ1211111-1-1-1-111111111−i−iii−i−iii-1-1-1-1-1-1-1-11-11−i−iii−i−iii1−i−iii−i−iii1-11-1
χ1311111-1-1-1-1111-1-1-1-11ii−i−iii−i−i-1-1-1-111111-11ii−i−iii−i−i-1−i−iii−i−iii1-1-11
χ1411111-1-1-1-1111-1-1-1-11ii−i−i−i−iii-1-1-1-11111-111ii−i−i−i−iii-1−i−iiiii−i−i-111-1
χ1511111-1-1-1-1111-1-1-1-11−i−iiiii−i−i-1-1-1-11111-111−i−iiiii−i−i-1ii−i−i−i−iii-111-1
χ1611111-1-1-1-1111-1-1-1-11−i−iii−i−iii-1-1-1-111111-11−i−iii−i−iii-1ii−i−iii−i−i1-1-11
χ17222222-2-222222222-2000000002-22-222-2-200-200000000-2000000000000
χ18222222-2-22222-2-2-2-2-2000000002-22-2-2-22200-2000000002000000000000
χ1922222-222-22222222-200000000-22-22-2-22200-200000000-2000000000000
χ2022222-222-2222-2-2-2-2-200000000-22-2222-2-200-2000000002000000000000
χ212222-12222-1-1-10000222222222-1-1-1-1000022-1-1-1-1-1-1-1-1-1000000000-1-100
χ222222-12222-1-1-1000022222-2-2-2-2-1-1-1-10000-2-2-1-1-1-1-111110000000001100
χ232222-12222-1-1-100002-2-2-2-22222-1-1-1-10000-2-2-11111-1-1-1-10000000001100
χ242222-12222-1-1-100002-2-2-2-2-2-2-2-2-1-1-1-1000022-111111111000000000-1-100
χ252222-1-2-2-2-2-1-1-1000022i2i−2i−2i2i2i−2i−2i111100002-2-1−i−iii−i−iii000000000-1100
χ262222-1-2-2-2-2-1-1-1000022i2i−2i−2i−2i−2i2i2i11110000-22-1−i−iiiii−i−i0000000001-100
χ272222-1-2-2-2-2-1-1-100002−2i−2i2i2i2i2i−2i−2i11110000-22-1ii−i−i−i−iii0000000001-100
χ282222-1-2-2-2-2-1-1-100002−2i−2i2i2i−2i−2i2i2i111100002-2-1ii−i−iii−i−i000000000-1100
χ2922-2-22200-22-2-222-2-202−22−2000020-202-2000002−22−2000002−22−200000000
χ3022-2-22200-22-2-222-2-20−22−22000020-202-200000−22−2200000−22−2200000000
χ3122-2-22200-22-2-2-2-22202−22−2000020-20-22000002−22−200000−22−2200000000
χ3222-2-22200-22-2-2-2-2220−22−22000020-20-2200000−22−22000002−22−200000000
χ3322-2-22-20022-2-222-2-20i2−i2−i2i20000-2020-2200000i2−i2−i2i200000i2−i2−i2i200000000
χ3422-2-22-20022-2-222-2-20−i2i2i2−i20000-2020-2200000−i2i2i2−i200000−i2i2i2−i200000000
χ3522-2-22-20022-2-2-2-2220i2−i2−i2i20000-20202-200000i2−i2−i2i200000−i2i2i2−i200000000
χ3622-2-22-20022-2-2-2-2220−i2i2i2−i20000-20202-200000−i2i2i2−i200000i2−i2−i2i200000000
χ372-2-22202-20-22-22i−2i2i−2i00000i2−i2i2−i20-202002i−2i0000000i2−i2i2−i2000002−22−20000
χ382-2-22202-20-22-22i−2i2i−2i00000−i2i2−i2i20-202002i−2i0000000−i2i2−i2i200000−22−220000
χ392-2-22202-20-22-2−2i2i−2i2i00000i2−i2i2−i20-20200−2i2i0000000i2−i2i2−i200000−22−220000
χ402-2-22202-20-22-2−2i2i−2i2i00000−i2i2−i2i20-20200−2i2i0000000−i2i2−i2i2000002−22−20000
χ412-2-2220-220-22-22i−2i2i−2i000002−2−22020-200−2i2i00000002−2−2200000−i2i2i2−i20000
χ422-2-2220-220-22-22i−2i2i−2i00000−222−2020-200−2i2i0000000−222−200000i2−i2−i2i20000
χ432-2-2220-220-22-2−2i2i−2i2i000002−2−22020-2002i−2i00000002−2−2200000i2−i2−i2i20000
χ442-2-2220-220-22-2−2i2i−2i2i00000−222−2020-2002i−2i0000000−222−200000−i2i2i2−i20000
χ454444-24-4-44-2-2-20000-400000000-22-220000002000000000000000000000
χ464444-2-444-4-2-2-20000-4000000002-22-20000002000000000000000000000
χ4744-4-4-2400-4-2220000022−2222−220000-20200000000−22−2200000000000000000
χ4844-4-4-2400-4-22200000−2222−22220000-202000000002−22−200000000000000000
χ4944-4-4-2-4004-222000002i2−2i2−2i22i2000020-200000000−i2i2i2−i200000000000000000
χ5044-4-4-2-4004-22200000−2i22i22i2−2i2000020-200000000i2−i2−i2i200000000000000000
χ514-44-440000-4-444i−4i−4i4i00000000000000000000000000000000000000000
χ524-44-440000-4-44−4i4i4i−4i00000000000000000000000000000000000000000
χ534-4-44-204-402-220000000002i2−2i22i2−2i2020-200000000000−i2i2−i2i20000000000000
χ544-4-44-204-402-22000000000−2i22i2−2i22i2020-200000000000i2−i2i2−i20000000000000
χ554-4-44-20-4402-2200000000022−22−22220-20200000000000−222−20000000000000
χ564-4-44-20-4402-22000000000−222222−220-202000000000002−2−220000000000000
χ578-88-8-4000044-4000000000000000000000000000000000000000000000

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