Finite Group Databasebeta

← Group #13180671

Character table — Group #13180671

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11114444444444444444669999999999991616161616161616161616161616161624242424363636363636363636363636363636363636363636363636545454545454
order12443333666612121212121212122422448888888833336666121212121212121266121266661212121224242424242424242424242424242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111-1-1-1-1iiii−i−i−i−i11111111111111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1ii−i−i
χ41111111111111111111111-1-1-1-1−i−i−i−iiiii11111111111111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1−i−iii
χ5111111−1−i32−1+i3211−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i3211111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32111111
χ6111111−1−i32−1+i3211−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i32111111-1-1-1-1-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-1-1-1
χ7111111−1−i32−1+i3211−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i3211-1-1-1-1iiii−i−i−i−i−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111+i321+i321−i321−i321+i321+i321−i321−i32ζ22ζ22ζ22ζ22ζ14ζ14ζ14ζ14−ζ22−ζ22−ζ22−ζ22−ζ14−ζ14−ζ14−ζ14-1-1ii−i−i
χ8111111−1−i32−1+i3211−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i3211-1-1-1-1−i−i−i−iiiii−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111+i321+i321−i321−i321+i321+i321−i321−i32−ζ22−ζ22−ζ22−ζ22−ζ14−ζ14−ζ14−ζ14ζ22ζ22ζ22ζ22ζ14ζ14ζ14ζ14-1-1−i−iii
χ9111111−1+i32−1−i3211−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i3211111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32111111
χ10111111−1+i32−1−i3211−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i32111111-1-1-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-1-1-1
χ11111111−1+i32−1−i3211−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i3211-1-1-1-1iiii−i−i−i−i−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111−i321−i321+i321+i321−i321−i321+i321+i32ζ14ζ14ζ14ζ14ζ22ζ22ζ22ζ22−ζ14−ζ14−ζ14−ζ14−ζ22−ζ22−ζ22−ζ22-1-1ii−i−i
χ12111111−1+i32−1−i3211−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i3211-1-1-1-1−i−i−i−iiiii−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111−i321−i321+i321+i321−i321−i321+i321+i32−ζ14−ζ14−ζ14−ζ14−ζ22−ζ22−ζ22−ζ22ζ14ζ14ζ14ζ14ζ22ζ22ζ22ζ22-1-1−i−iii
χ1311-1-111111111-1-1-1-1-1-1-1-1-1111-1-1ii−i−iii−i−i11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i-11i−ii−i
χ1411-1-111111111-1-1-1-1-1-1-1-1-1111-1-1−i−iii−i−iii11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1−i−iii−i−iii−i−iii−i−iii-11−ii−ii
χ1511-1-111111111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111-1-1111-11-1-11
χ1611-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-11111-1-111-1-11-1-111-1
χ1711-1-111−1−i32−1+i3211−1−i32−1+i32-1-1-1-11+i321+i321−i321−i32-1111-1-1ii−i−iii−i−i−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14-11i−ii−i
χ1811-1-111−1−i32−1+i3211−1−i32−1+i32-1-1-1-11+i321+i321−i321−i32-1111-1-1−i−iii−i−iii−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14-11−ii−ii
χ1911-1-111−1−i32−1+i3211−1−i32−1+i32-1-1-1-11+i321+i321−i321−i32-11-1-11111-1-1-1-111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-11-1-11
χ2011-1-111−1−i32−1+i3211−1−i32−1+i32-1-1-1-11+i321+i321−i321−i32-11-1-111-1-11111-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1-111-1
χ2111-1-111−1+i32−1−i3211−1+i32−1−i32-1-1-1-11−i321−i321+i321+i32-1111-1-1ii−i−iii−i−i−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ22-11i−ii−i
χ2211-1-111−1+i32−1−i3211−1+i32−1−i32-1-1-1-11−i321−i321+i321+i32-1111-1-1−i−iii−i−iii−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ22-11−ii−ii
χ2311-1-111−1+i32−1−i3211−1+i32−1−i32-1-1-1-11−i321−i321+i321+i32-11-1-11111-1-1-1-111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-11-1-11
χ2411-1-111−1+i32−1−i3211−1+i32−1−i32-1-1-1-11−i321−i321+i321+i32-11-1-111-1-11111-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1-111-1
χ252-22i−2i22-1-1-2-2112i2i−2i−2ii−ii−i002-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-1-1-1-11111ii−i−iii−i−i00001-11-1i−ii−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13000000
χ262-22i−2i22-1-1-2-2112i2i−2i−2ii−ii−i002-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-1-1-1-11111ii−i−iii−i−i00001-11-1i−ii−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13000000
χ272-22i−2i22-1-1-2-2112i2i−2i−2ii−ii−i00-22−2i2i−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23-1-1-1-11111ii−i−iii−i−i0000-11-11−ii−ii−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23000000
χ282-22i−2i22-1-1-2-2112i2i−2i−2ii−ii−i00-22−2i2i2ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ23-1-1-1-11111ii−i−iii−i−i0000-11-11−ii−iiζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23000000
χ292-22i−2i221+i321−i32-2-2−1−i32−1+i322i2i−2i−2iζ22−ζ22ζ14−ζ14002-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ131+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ140000−1−i321+i32−1+i321−i32ζ22−ζ22ζ14−ζ14−ζ7ζ7ζ13−ζ13−ζ23ζ23ζ5−ζ5−ζ7ζ7ζ13−ζ13−ζ23ζ23ζ5−ζ5000000
χ302-22i−2i221+i321−i32-2-2−1−i32−1+i322i2i−2i−2iζ22−ζ22ζ14−ζ14002-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ131+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ140000−1−i321+i32−1+i321−i32ζ22−ζ22ζ14−ζ14ζ7−ζ7−ζ13ζ13ζ23−ζ23−ζ5ζ5ζ7−ζ7−ζ13ζ13ζ23−ζ23−ζ5ζ5000000
χ312-22i−2i221+i321−i32-2-2−1−i32−1+i322i2i−2i−2iζ22−ζ22ζ14−ζ1400-22−2i2i−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ231+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ1400001+i32−1−i321−i32−1+i32−ζ22ζ22−ζ14ζ14ζ13−ζ13ζ7−ζ7ζ5−ζ5ζ23−ζ23−ζ13ζ13−ζ7ζ7−ζ5ζ5−ζ23ζ23000000
χ322-22i−2i221+i321−i32-2-2−1−i32−1+i322i2i−2i−2iζ22−ζ22ζ14−ζ1400-22−2i2i2ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ231+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32ζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ1400001+i32−1−i321−i32−1+i32−ζ22ζ22−ζ14ζ14−ζ13ζ13−ζ7ζ7−ζ5ζ5−ζ23ζ23ζ13−ζ13ζ7−ζ7ζ5−ζ5ζ23−ζ23000000
χ332-22i−2i221−i321+i32-2-2−1+i32−1−i322i2i−2i−2iζ14−ζ14ζ22−ζ22002-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ131−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ220000−1+i321−i32−1−i321+i32ζ14−ζ14ζ22−ζ22−ζ23ζ23ζ5−ζ5−ζ7ζ7ζ13−ζ13−ζ23ζ23ζ5−ζ5−ζ7ζ7ζ13−ζ13000000
χ342-22i−2i221−i321+i32-2-2−1+i32−1−i322i2i−2i−2iζ14−ζ14ζ22−ζ22002-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ131−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ220000−1+i321−i32−1−i321+i32ζ14−ζ14ζ22−ζ22ζ23−ζ23−ζ5ζ5ζ7−ζ7−ζ13ζ13ζ23−ζ23−ζ5ζ5ζ7−ζ7−ζ13ζ13000000
χ352-22i−2i221−i321+i32-2-2−1+i32−1−i322i2i−2i−2iζ14−ζ14ζ22−ζ2200-22−2i2i−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ231−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ2200001−i32−1+i321+i32−1−i32−ζ14ζ14−ζ22ζ22ζ5−ζ5ζ23−ζ23ζ13−ζ13ζ7−ζ7−ζ5ζ5−ζ23ζ23−ζ13ζ13−ζ7ζ7000000
χ362-22i−2i221−i321+i32-2-2−1+i32−1−i322i2i−2i−2iζ14−ζ14ζ22−ζ2200-22−2i2i2ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ231−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32ζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ2200001−i32−1+i321+i32−1−i32−ζ14ζ14−ζ22ζ22−ζ5ζ5−ζ23ζ23−ζ13ζ13−ζ7ζ7ζ5−ζ5ζ23−ζ23ζ13−ζ13ζ7−ζ7000000
χ372-2−2i2i22-1-1-2-211−2i−2i2i2i−ii−ii002-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23-1-1-1-11111−i−iii−i−iii00001-11-1−ii−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23000000
χ382-2−2i2i22-1-1-2-211−2i−2i2i2i−ii−ii002-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23-1-1-1-11111−i−iii−i−iii00001-11-1−ii−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23000000
χ392-2−2i2i22-1-1-2-211−2i−2i2i2i−ii−ii00-222i−2i2ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ13-1-1-1-11111−i−iii−i−iii0000-11-11i−ii−iζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13000000
χ402-2−2i2i22-1-1-2-211−2i−2i2i2i−ii−ii00-222i−2i−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13-1-1-1-11111−i−iii−i−iii0000-11-11i−ii−i−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.