Finite Group Databasebeta

← Group #70940

Character table — Group #70940

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222222222222222222244444444444444444444444444444444444242424244848
order122234444666888812121212242424242424242444444888888121212121212121212121212242424242424242424242424888824
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1
χ31111111111111111111111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ5111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1
χ6111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11
χ7111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-11
χ8111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-1
χ92222222-2-2222222222222222222200-200-2-20000-2-2-2-200000000-2-2-2-200000000000000
χ102222222-2-2222-2-2-2-22222-2-2-2-2-2-2-2-200-200220000-2-2-2-200000000222200000000000000
χ1122222-2-2222220000-2-2-2-20000000022-2-2-200000022-2-22222-2-2-2-2000000000000000000
χ1222222-2-2222220000-2-2-2-200000000-2-2-22200000022-2-2-2-2-2-22222000000000000000000
χ1322222-2-2-2-22220000-2-2-2-20000000000200002i2i−2i−2i-2-2220000000000002i2i2i2i−2i−2i−2i−2i000000
χ1422222-2-2-2-22220000-2-2-2-2000000000020000−2i−2i2i2i-2-222000000000000−2i−2i−2i−2i2i2i2i2i000000
χ152222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000
χ162222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-22-2-222-2-2-2-2-1-1-1-111111111-1-1-1-111111111000000
χ172222-12222-1-1-1-2-2-2-2-1-1-1-11111111122222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000
χ182222-12222-1-1-1-2-2-2-2-1-1-1-111111111-2-22-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-1000000
χ192222-122-2-2-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-200-2-200001111−i3−i3i3i3−i3−i3i3i31111−i3−i3i3i3−i3−i3i3i3000000
χ202222-122-2-2-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-200-2-200001111i3i3−i3−i3i3i3−i3−i31111i3i3−i3−i3i3i3−i3−i3000000
χ212222-122-2-2-1-1-1-2-2-2-2-1-1-1-11111111100-2002200001111−i3−i3i3i3−i3−i3i3i3-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000
χ222222-122-2-2-1-1-1-2-2-2-2-1-1-1-11111111100-2002200001111i3i3−i3−i3i3i3−i3−i3-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000
χ232222-1-2-222-1-1-1000011113333−3−3−3−322-2-2-2000000-1-111-1-1-1-1111133−3−333−3−3−3−333000000
χ242222-1-2-222-1-1-1000011113333−3−3−3−3-2-2-222000000-1-1111111-1-1-1-133−3−3−3−33333−3−3000000
χ252222-1-2-222-1-1-100001111−3−3−3−3333322-2-2-2000000-1-111-1-1-1-11111−3−333−3−33333−3−3000000
χ262222-1-2-222-1-1-100001111−3−3−3−33333-2-2-222000000-1-1111111-1-1-1-1−3−33333−3−3−3−333000000
χ272222-1-2-2-2-2-1-1-1000011113333−3−3−3−300200002i2i−2i−2i11-1-1−i3−i3i3i3i3i3−i3−i3−3−333−i−i−i−iiiii000000
χ282222-1-2-2-2-2-1-1-1000011113333−3−3−3−30020000−2i−2i2i2i11-1-1i3i3−i3−i3−i3−i3i3i3−3−333iiii−i−i−i−i000000
χ292222-1-2-2-2-2-1-1-100001111−3−3−3−3333300200002i2i−2i−2i11-1-1i3i3−i3−i3−i3−i3i3i333−3−3−i−i−i−iiiii000000
χ302222-1-2-2-2-2-1-1-100001111−3−3−3−333330020000−2i−2i2i2i11-1-1−i3−i3i3i3i3i3−i3−i333−3−3iiii−i−i−i−i000000
χ3122-2-22-22002-2-22i2i−2i−2i-2-2222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000−i2i22−200
χ3222-2-22-22002-2-22i2i−2i−2i-2-2222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000i2−i2−2200
χ3322-2-22-22002-2-2−2i−2i2i2i-2-222−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000−i2i2−2200
χ3422-2-22-22002-2-2−2i−2i2i2i-2-222−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000i2−i22−200
χ352-22-22002-2-22-2−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i20002i−2i−i2i22−22−22-20000002i−2i2i−2i−i2i2−i2i22−22−22−22−2000000
χ362-22-22002-2-22-2−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2000−2i2i−i2i2−22−222-2000000−2i2i−2i2i−i2i2−i2i2−22−22−22−22000000
χ372-22-22002-2-22-2i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i20002i−2ii2−i2−22−222-20000002i−2i2i−2ii2−i2i2−i2−22−22−22−22000000
χ382-22-22002-2-22-2i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2000−2i2ii2−i22−22−22-2000000−2i2i−2i2ii2−i2i2−i22−22−22−22−2000000
χ392-22-2200-22-22-2−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i22-2000i2−i2−i2i2i2−i2-22002-22-20000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000
χ402-22-2200-22-22-2−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i2-22000i2−i2i2−i2−i2i2-2200-22-220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000
χ412-22-2200-22-22-2i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i22-2000−i2i2i2−i2−i2i2-22002-22-20000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000
χ422-22-2200-22-22-2i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i2-22000−i2i2−i2i2i2−i2-2200-22-220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000
χ432-22-2-1002-21-11−i2i2−i2i23−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ230002i−2i−i2i22−22−2-113−3i3−i3−i3i3−ii−iiζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ442-22-2-1002-21-11−i2i2−i2i23−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000−2i2i−i2i2−22−22-113−3−i3i3i3−i3i−ii−iζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ452-22-2-1002-21-11−i2i2−i2i2−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ70002i−2i−i2i22−22−2-11−33−i3i3i3−i3−ii−iiζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ462-22-2-1002-21-11−i2i2−i2i2−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000−2i2i−i2i2−22−22-11−33i3−i3−i3i3i−ii−iζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ472-22-2-1002-21-11i2−i2i2−i23−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ230002i−2ii2−i2−22−22-113−3i3−i3−i3i3−ii−ii−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7000000
χ482-22-2-1002-21-11i2−i2i2−i23−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000−2i2ii2−i22−22−2-113−3−i3i3i3−i3i−ii−i−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
χ492-22-2-1002-21-11i2−i2i2−i2−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ70002i−2ii2−i2−22−22-11−33−i3i3i3−i3−ii−ii−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23000000
χ502-22-2-1002-21-11i2−i2i2−i2−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000−2i2ii2−i22−22−2-11−33i3−i3−i3i3i−ii−i−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23000000
χ512-22-2-100-221-11−i2i2−i2i23−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ232-2000i2−i2−i2i2i2−i21-1−33-11-11−333−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ522-22-2-100-221-11−i2i2−i2i23−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23-22000i2−i2i2−i2−i2i21-1−331-11-13−3−33−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ532-22-2-100-221-11−i2i2−i2i2−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ72-2000i2−i2−i2i2i2−i21-13−3-11-113−3−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ542-22-2-100-221-11−i2i2−i2i2−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7-22000i2−i2i2−i2−i2i21-13−31-11-1−333−3−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ552-22-2-100-221-11i2−i2i2−i23−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ232-2000−i2i2i2−i2−i2i21-1−33-11-11−333−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000
χ562-22-2-100-221-11i2−i2i2−i23−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23-22000−i2i2−i2i2i2−i21-1−331-11-13−3−33ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000
χ572-22-2-100-221-11i2−i2i2−i2−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ72-2000−i2i2i2−i2−i2i21-13−3-11-113−3−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000
χ582-22-2-100-221-11i2−i2i2−i2−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7-22000−i2i2−i2i2i2−i21-13−31-11-1−333−3ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000
χ5944-4-444-4004-4-4000044-4-40000000000000000000000000000000000000000000000000
χ6044-4-4-24-400-2220000-2-222−2i3−2i32i32i32i32i3−2i3−2i300000000000000000000000000000000000000000
χ6144-4-4-24-400-2220000-2-2222i32i3−2i3−2i3−2i3−2i32i32i300000000000000000000000000000000000000000
χ6244-4-4-2-4400-2224i4i−4i−4i22-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000
χ6344-4-4-2-4400-222−4i−4i4i4i22-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000
χ644-4-4440000-4-4422−22−2222000022−22−222222−22−222200000000000000000000000000000000000000000
χ654-4-4440000-4-44−222222−220000−222222−22−222222−2200000000000000000000000000000000000000000
χ664-4-44-2000022-222−22−222223−23−23232ζ5−2ζ7−2ζ5+2ζ7−2ζ5+2ζ72ζ5−2ζ72ζ13−2ζ23−2ζ13+2ζ23−2ζ13+2ζ232ζ13−2ζ2300000000000000000000000000000000000000000
χ674-4-44-2000022-222−22−2222−232323−232ζ13−2ζ23−2ζ13+2ζ23−2ζ13+2ζ232ζ13−2ζ232ζ5−2ζ7−2ζ5+2ζ7−2ζ5+2ζ72ζ5−2ζ700000000000000000000000000000000000000000
χ684-4-44-2000022-2−222222−2223−23−2323−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ7−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ2300000000000000000000000000000000000000000
χ694-4-44-2000022-2−222222−22−232323−23−2ζ13+2ζ232ζ13−2ζ232ζ13−2ζ23−2ζ13+2ζ23−2ζ5+2ζ72ζ5−2ζ72ζ5−2ζ7−2ζ5+2ζ700000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.