Finite Group Databasebeta

← Group #72018

Character table — Group #72018

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222222222222222222244444444444444444444444444444444442424242424242424
order122222344446668888121212122424242424242424224466666688888812121212121224242424242424242424242422448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ611111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ811111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ91-11-11-111-11-1-1-11ii−i−i11-1-1iiii−i−i−i−i1-11-11-111-1-1i−iii−i−i1-111-1-1ii−i−iiiii−i−i−i−i1-1i−i1-1i−i
χ101-11-11-111-11-1-1-11ii−i−i11-1-1iiii−i−i−i−i1-11-11-111-1-1i−iii−i−i1-111-1-1ii−i−iiiii−i−i−i−i-11−ii-11−ii
χ111-11-11-111-11-1-1-11ii−i−i11-1-1iiii−i−i−i−i-11-111-1-1-111i−i−i−iii1-1-1-111ii−i−i−i−i−i−iiiii1-1i−i-11−ii
χ121-11-11-111-11-1-1-11ii−i−i11-1-1iiii−i−i−i−i-11-111-1-1-111i−i−i−iii1-1-1-111ii−i−i−i−i−i−iiiii-11−ii1-1i−i
χ131-11-11-111-11-1-1-11−i−iii11-1-1−i−i−i−iiiii1-11-11-111-1-1−ii−i−iii1-111-1-1−i−iii−i−i−i−iiiii1-1−ii1-1−ii
χ141-11-11-111-11-1-1-11−i−iii11-1-1−i−i−i−iiiii1-11-11-111-1-1−ii−i−iii1-111-1-1−i−iii−i−i−i−iiiii-11i−i-11i−i
χ151-11-11-111-11-1-1-11−i−iii11-1-1−i−i−i−iiiii-11-111-1-1-111−iiii−i−i1-1-1-111−i−iiiiiii−i−i−i−i1-1−ii-11i−i
χ161-11-11-111-11-1-1-11−i−iii11-1-1−i−i−i−iiiii-11-111-1-1-111−iiii−i−i1-1-1-111−i−iiiiiii−i−i−i−i-11i−i1-1−ii
χ172222222-2-2-2-22220000-2-2-2-2000000000000220000002i−2i2i−2i-2-2000000002i2i−2i−2i2i2i−2i−2i00000000
χ182222222-2-2-2-22220000-2-2-2-200000000000022000000−2i2i−2i2i-2-200000000−2i−2i2i2i−2i−2i2i2i00000000
χ19222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ20222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111122-2-2-2-2-1-11111-1-1-1-11111111100000000
χ21222222-12222-1-1-1-2-2-2-2-1-1-1-1111111112222-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-111111111111100000000
χ22222222-12222-1-1-1-2-2-2-2-1-1-1-111111111-2-2-2-2-1-11111-2-22222-1-111111111-1-1-1-1-1-1-1-100000000
χ23222222-1-2-2-2-2-1-1-10000111133−3−333−3−30000-1-1−i3i3−i3i3002i−2i2i−2i11−i3i3−i3i33−33−3−i−iii−i−iii00000000
χ24222222-1-2-2-2-2-1-1-10000111133−3−333−3−30000-1-1i3−i3i3−i300−2i2i−2i2i11i3−i3i3−i33−33−3ii−i−iii−i−i00000000
χ25222222-1-2-2-2-2-1-1-100001111−3−333−3−3330000-1-1−i3i3−i3i300−2i2i−2i2i11−i3i3−i3i3−33−33ii−i−iii−i−i00000000
χ26222222-1-2-2-2-2-1-1-100001111−3−333−3−3330000-1-1i3−i3i3−i3002i−2i2i−2i11i3−i3i3−i3−33−33−i−iii−i−iii00000000
χ272222-2-2222-2-222222222222222222220000-2-20000-2-20000-2-20000-2-2-2-20000000000000000
χ282222-2-2222-2-2222-2-2-2-22222-2-2-2-2-2-2-2-20000-2-20000220000-2-2000022220000000000000000
χ292222-2-22-2-2222220000-2-2-2-20000000022-2-2-2-2222200000022-2-2-2-200000000000000000000
χ302222-2-22-2-2222220000-2-2-2-200000000-2-222-2-2-2-2-2-200000022222200000000000000000000
χ312222-2-2-122-2-2-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000011−i3i3−i3i3-2-2000011i3−i3i3−i31111−i3i3−i3i3−i3i3−i3i300000000
χ322222-2-2-122-2-2-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000011i3−i3i3−i3-2-2000011−i3i3−i3i31111i3−i3i3−i3i3−i3i3−i300000000
χ332222-2-2-122-2-2-1-1-1-2-2-2-2-1-1-1-111111111000011−i3i3−i3i322000011i3−i3i3−i3-1-1-1-1i3−i3i3−i3i3−i3i3−i300000000
χ342222-2-2-122-2-2-1-1-1-2-2-2-2-1-1-1-111111111000011i3−i3i3−i322000011−i3i3−i3i3-1-1-1-1−i3i3−i3i3−i3i3−i3i300000000
χ352222-2-2-1-2-222-1-1-10000111133−3−333−3−322-2-211-1-1-1-1000000-1-11111−33−333−3−333−3−3300000000
χ362222-2-2-1-2-222-1-1-10000111133−3−333−3−3-2-222111111000000-1-1-1-1-1-1−33−33−333−3−333−300000000
χ372222-2-2-1-2-222-1-1-100001111−3−333−3−33322-2-211-1-1-1-1000000-1-111113−33−3−333−3−333−300000000
χ382222-2-2-1-2-222-1-1-100001111−3−333−3−333-2-222111111000000-1-1-1-1-1-13−33−33−3−333−3−3300000000
χ392-22-22-22-22-22-2-220000-2-2220000000000002-20000002-2-22-220000000022-2-2-2-22200000000
χ402-22-22-22-22-22-2-220000-2-2220000000000002-2000000-222-2-2200000000-2-22222-2-200000000
χ412-22-22-2-12-22-211-12i2i−2i−2i-1-111−i−i−i−iiiii2-22-2-11-1-1112i−2i2i2i−2i−2i-11-1-111−i−iii−i−i−i−iiiii00000000
χ422-22-22-2-12-22-211-12i2i−2i−2i-1-111−i−i−i−iiiii-22-22-1111-1-12i−2i−2i−2i2i2i-1111-1-1−i−iiiiiii−i−i−i−i00000000
χ432-22-22-2-12-22-211-1−2i−2i2i2i-1-111iiii−i−i−i−i2-22-2-11-1-111−2i2i−2i−2i2i2i-11-1-111ii−i−iiiii−i−i−i−i00000000
χ442-22-22-2-12-22-211-1−2i−2i2i2i-1-111iiii−i−i−i−i-22-22-1111-1-1−2i2i2i2i−2i−2i-1111-1-1ii−i−i−i−i−i−iiiii00000000
χ452-22-22-2-1-22-2211-1000011-1-1−i3−i3i3i3i3i3−i3−i30000-11−i3i3i3−i3002-2-221-1−i3i3i3−i3−i3i3i3−i3-1-11111-1-100000000
χ462-22-22-2-1-22-2211-1000011-1-1−i3−i3i3i3i3i3−i3−i30000-11i3−i3−i3i300-222-21-1i3−i3−i3i3−i3i3i3−i311-1-1-1-11100000000
χ472-22-22-2-1-22-2211-1000011-1-1i3i3−i3−i3−i3−i3i3i30000-11−i3i3i3−i300-222-21-1−i3i3i3−i3i3−i3−i3i311-1-1-1-11100000000
χ482-22-22-2-1-22-2211-1000011-1-1i3i3−i3−i3−i3−i3i3i30000-11i3−i3−i3i3002-2-221-1i3−i3−i3i3i3−i3−i3i3-1-11111-1-100000000
χ492-22-2-2222-2-22-2-222i2i−2i−2i22-2-22i2i2i2i−2i−2i−2i−2i0000-220000−2i2i0000-220000−2i−2i2i2i0000000000000000
χ502-22-2-2222-2-22-2-22−2i−2i2i2i22-2-2−2i−2i−2i−2i2i2i2i2i0000-2200002i−2i0000-2200002i2i−2i−2i0000000000000000
χ512-22-2-222-222-2-2-220000-2-222000000002-2-22-2222-2-20000002-2-2-22200000000000000000000
χ522-22-2-222-222-2-2-220000-2-22200000000-222-2-22-2-2220000002-222-2-200000000000000000000
χ532-22-2-22-12-2-2211-12i2i−2i−2i-1-111−i−i−i−iiiii00001-1−i3i3i3−i3−2i2i00001-1i3−i3−i3i3ii−i−i3−33−3−33−3300000000
χ542-22-2-22-12-2-2211-12i2i−2i−2i-1-111−i−i−i−iiiii00001-1i3−i3−i3i3−2i2i00001-1−i3i3i3−i3ii−i−i−33−333−33−300000000
χ552-22-2-22-12-2-2211-1−2i−2i2i2i-1-111iiii−i−i−i−i00001-1−i3i3i3−i32i−2i00001-1i3−i3−i3i3−i−iii−33−333−33−300000000
χ562-22-2-22-12-2-2211-1−2i−2i2i2i-1-111iiii−i−i−i−i00001-1i3−i3−i3i32i−2i00001-1−i3i3i3−i3−i−iii3−33−3−33−3300000000
χ572-22-2-22-1-222-211-1000011-1-1−i3−i3i3i3i3i3−i3−i32-2-221-1-1-111000000-1111-1-1i3−i3−i3i3−i3i3i3−i3i3−i3−i3i300000000
χ582-22-2-22-1-222-211-1000011-1-1−i3−i3i3i3i3i3−i3−i3-222-21-111-1-1000000-11-1-111i3−i3−i3i3i3−i3−i3i3−i3i3i3−i300000000
χ592-22-2-22-1-222-211-1000011-1-1i3i3−i3−i3−i3−i3i3i32-2-221-1-1-111000000-1111-1-1−i3i3i3−i3i3−i3−i3i3−i3i3i3−i300000000
χ602-22-2-22-1-222-211-1000011-1-1i3i3−i3−i3−i3−i3i3i3-222-21-111-1-1000000-11-1-111−i3i3i3−i3−i3i3i3−i3i3−i3−i3i300000000
χ6144-4-400400004-4-4−2i22i2−2i22i20000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000000000
χ6244-4-400400004-4-42i2−2i22i2−2i200002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000000000
χ6344-4-400-20000-222−2i22i2−2i22i223−2323−232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23000000000000000000000000000000000000000000
χ6444-4-400-20000-222−2i22i2−2i22i2−2323−23232ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7000000000000000000000000000000000000000000
χ6544-4-400-20000-2222i2−2i22i2−2i223−2323−23−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23000000000000000000000000000000000000000000
χ6644-4-400-20000-2222i2−2i22i2−2i2−2323−2323−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7000000000000000000000000000000000000000000
χ674-4-440040000-44-422−22−2222000022−2222−22−2222−2222000000000000000000000000000000000000000000
χ684-4-440040000-44-4−222222−220000−2222−222222−2222−22000000000000000000000000000000000000000000
χ694-4-4400-200002-2222−22−222223−23−23232ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000000000000000000000
χ704-4-4400-200002-2222−22−2222−232323−232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23000000000000000000000000000000000000000000
χ714-4-4400-200002-22−222222−2223−23−2323−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ72ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000000000000000000000
χ724-4-4400-200002-22−222222−22−232323−23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23000000000000000000000000000000000000000000

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