Finite Group Databasebeta

← Group #70612

Character table — Group #70612

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111111122222222222222222222444444444444666666666666666688888888888824242424
order12222222344446666666888888881212121224242424242424244444444488888888444412121212121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ911-1-11-11-111-11-11-1-1-1-1111111-1-1-1-11-1-111111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i1-11-111-1-111-1-1i−ii−i
χ1011-1-11-11-111-11-11-1-1-1-1111111-1-1-1-11-1-111111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i-11-11-1-111-1-111−ii−ii
χ1111-1-11-11-111-11-11-1-1-1-1111111-1-1-1-11-1-111111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii1-11-111-1-111-1-1−ii−ii
χ1211-1-11-11-111-11-11-1-1-1-1111111-1-1-1-11-1-111111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii-11-11-1-111-1-111i−ii−i
χ1311-1-11-11-111-11-11-1-1-1-111-1-1-1-111111-1-11-1-1-1-11111ii−i−iii−i−i−i−i−i−iiiii1-1-1111-1-1-1-111i−i−ii
χ1411-1-11-11-111-11-11-1-1-1-111-1-1-1-111111-1-11-1-1-1-11111ii−i−iii−i−i−i−i−i−iiiii-111-1-1-11111-1-1−iii−i
χ1511-1-11-11-111-11-11-1-1-1-111-1-1-1-111111-1-11-1-1-1-11111−i−iii−i−iiiiiii−i−i−i−i1-1-1111-1-1-1-111−iii−i
χ1611-1-11-11-111-11-11-1-1-1-111-1-1-1-111111-1-11-1-1-1-11111−i−iii−i−iiiiiii−i−i−i−i-111-1-1-11111-1-1i−i−ii
χ17222222222-2-2-2-2222222200000000-2-2-2-2000000002222-2-2-2-2000000000000000000000000
χ18222222222-2-2-2-2222222200000000-2-2-2-200000000-2-2-2-22222000000000000000000000000
χ1922222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ2022222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ2122222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111000000000000000022-2-2-1-1-1-111110000
χ2222222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111110000000000000000-2-2221111-1-1-1-10000
χ23222-2-22-2-220000222-2-2-2-222−2−222−2−2000022−2−222−2−22-22-2000022−2−222−2−20000000000000000
χ24222-2-22-2-220000222-2-2-2-222−2−222−2−2000022−2−222−2−2-22-220000−2−222−2−2220000000000000000
χ25222-2-22-2-220000222-2-2-2-2−2−222−2−2220000−2−222−2−2222-22-20000−2−222−2−2220000000000000000
χ26222-2-22-2-220000222-2-2-2-2−2−222−2−2220000−2−222−2−222-22-22000022−2−222−2−20000000000000000
χ2722-22-2-2-22200002-2-222-2-222−2−2−2−222000022−2−2−2−2222i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i20000000000000000
χ2822-22-2-2-22200002-2-222-2-222−2−2−2−222000022−2−2−2−222−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i20000000000000000
χ2922-22-2-2-22200002-2-222-2-2−2−22222−2−20000−2−22222−2−22i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i20000000000000000
χ3022-22-2-2-22200002-2-222-2-2−2−22222−2−20000−2−22222−2−2−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i20000000000000000
χ3122-2-22-22-22-22-222-2-2-2-22200000000-222-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ3222-2-22-22-22-22-222-2-2-2-22200000000-222-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ3322-2-22-22-2-12-22-2-11111-1-12222-2-2-2-2-111-1-1-1-1-1111100000000000000002-22-2-1-111-1-1110000
χ3422-2-22-22-2-12-22-2-11111-1-12222-2-2-2-2-111-1-1-1-1-111110000000000000000-22-2211-1-111-1-10000
χ3522-2-22-22-2-12-22-2-11111-1-1-2-2-2-22222-111-11111-1-1-1-100000000000000002-2-22-1-11111-1-10000
χ3622-2-22-22-2-12-22-2-11111-1-1-2-2-2-22222-111-11111-1-1-1-10000000000000000-222-211-1-1-1-1110000
χ372-2222-2-2-222-2-22-22-22-22-20000000022-2-200000000000000002-22-22-22-20000000000000000
χ382-2222-2-2-222-2-22-22-22-22-20000000022-2-20000000000000000-22-22-22-220000000000000000
χ392-2222-2-2-22-222-2-22-22-22-22-22-22-22-2-2-2222-22-22-22-200000000000000000000000000000000
χ402-2222-2-2-22-222-2-22-22-22-2-22-22-22-22-2-222-22-22-22-2200000000000000000000000000000000
χ412-2222-2-2-2-1-222-21-11-11-112-22-22-22-211-1-1-11-11-11-11000000000000000000003−33−33−33−30000
χ422-2222-2-2-2-1-222-21-11-11-112-22-22-22-211-1-1-11-11-11-1100000000000000000000−33−33−33−330000
χ432-2222-2-2-2-1-222-21-11-11-11-22-22-22-2211-1-11-11-11-11-1000000000000000000003−33−3−33−330000
χ442-2222-2-2-2-1-222-21-11-11-11-22-22-22-2211-1-11-11-11-11-100000000000000000000−33−333−33−30000
χ452-22-2-2-22220000-22-2-22-222−2−222−2−2200002−2−222−2−2200002-22-22−2−222−2−220000000000000000
χ462-22-2-2-22220000-22-2-22-222−2−222−2−2200002−2−222−2−220000-22-22−222−2−222−20000000000000000
χ472-22-2-2-22220000-22-2-22-22−222−2−222−20000−222−2−222−200002-22-2−222−2−222−20000000000000000
χ482-22-2-2-22220000-22-2-22-22−222−2−222−20000−222−2−222−20000-22-222−2−222−2−220000000000000000
χ492-2-22-222-220000-2-222-2-222−2−22−222−200002−2−22−222−200002i−2i−2i2ii2−i2−i2i2−i2i2i2−i20000000000000000
χ502-2-22-222-220000-2-222-2-222−2−22−222−200002−2−22−222−20000−2i2i2i−2i−i2i2i2−i2i2−i2−i2i20000000000000000
χ512-2-22-222-220000-2-222-2-22−222−22−2−220000−222−22−2−2200002i−2i−2i2i−i2i2i2−i2i2−i2−i2i20000000000000000
χ522-2-22-222-220000-2-222-2-22−222−22−2−220000−222−22−2−220000−2i2i2i−2ii2−i2−i2i2−i2i2i2−i20000000000000000
χ532-2-2-222-22222-2-2-2-22-222-2000000002-22-200000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ542-2-2-222-22222-2-2-2-22-222-2000000002-22-20000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ552-2-2-222-222-2-222-2-22-222-22-22-2-22-22-22-222-22-2-22-2200000000000000000000000000000000
χ562-2-2-222-222-2-222-2-22-222-2-22-222-22-2-22-22-22-222-22-200000000000000000000000000000000
χ572-2-2-222-22-1-2-22211-11-1-112-22-2-22-221-11-1-11-111-11-1000000000000000000003−3−333−3−330000
χ582-2-2-222-22-1-2-22211-11-1-112-22-2-22-221-11-1-11-111-11-100000000000000000000−333−3−333−30000
χ592-2-2-222-22-1-2-22211-11-1-11-22-222-22-21-11-11-11-1-11-11000000000000000000003−3−33−333−30000
χ602-2-2-222-22-1-2-22211-11-1-11-22-222-22-21-11-11-11-1-11-1100000000000000000000−333−33−3−330000
χ6144444444-2-4-4-4-4-2-2-2-2-2-2-20000000022220000000000000000000000000000000000000000
χ62444-4-44-4-4-20000-2-2-222222222−22−222222−22−220000−2−222−2−22200000000000000000000000000000000
χ63444-4-44-4-4-20000-2-2-22222−22−222222−22−222222000022−2−222−2−200000000000000000000000000000000
χ6444-44-4-4-44-20000-222-2-2222222−22−22−22−2222220000−2−22222−2−200000000000000000000000000000000
χ6544-44-4-4-44-20000-222-2-222−22−2222222222−22−22000022−2−2−2−22200000000000000000000000000000000
χ6644-4-44-44-4-2-44-44-22222-2-2000000002-2-220000000000000000000000000000000000000000
χ674-4444-4-4-4-24-4-442-22-22-2200000000-2-2220000000000000000000000000000000000000000
χ684-44-4-4-444-200002-222-22-222−22−222222−22−22220000−222−2−222−200000000000000000000000000000000
χ694-44-4-4-444-200002-222-22-2−222222−22−222222−2200002−2−222−2−2200000000000000000000000000000000
χ704-4-44-444-4-2000022-2-222-222−22−2222−222222−220000−222−22−2−2200000000000000000000000000000000
χ714-4-44-444-4-2000022-2-222-2−222222−2222−22−222200002−2−22−222−200000000000000000000000000000000
χ724-4-4-444-44-244-4-422-22-2-2200000000-22-220000000000000000000000000000000000000000

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