Finite Group Databasebeta

← Group #13180890

Character table — Group #13180890

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size11222222233444444444666666666888888888888881212121212121212121216161616161616161616181818181818242424242424242424242424242424243636363648484848545472727272
order12233666644333666666244441212121233336666666666612121212121212121233666666662222446612121212121212121212121212126661266121224661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111-1111-1111111111111111111-11111-11111111111111111-1-1-1-1-1-11111-1-111111111-111-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111−1−i32−1+i321111−1−i32−1+i32111111111−1−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+i32111111−1−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+i32111111−1−i32−1+i3211−1−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+i3211−1−i32−1+i32−1−i32−1+i32
χ4111111111111−1−i32−1+i321111−1−i32−1+i32-1111-11111−1−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+i32-11111-1−1−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+i3211-1-1-1-11+i321−i3211−1−i32−1+i321+i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-111-11+i321−i321+i321−i32-1-11+i321−i321+i321−i32
χ5111111111111−1+i32−1−i321111−1+i32−1−i32111111111−1+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−i32111111−1+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−i32111111−1+i32−1−i3211−1+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−i3211−1+i32−1−i32−1+i32−1−i32
χ6111111111111−1+i32−1−i321111−1+i32−1−i32-1111-11111−1+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−i32-11111-1−1+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−i3211-1-1-1-11−i321+i3211−1+i32−1−i321−i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-111-11−i321+i321−i321+i32-1-11−i321+i321−i321+i32
χ7111111111-1-1111111111111-11-1-1-1-111111111111111111111-1-1-1-11111111111-1-11-11-11111-1-111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1
χ8111111111-1-1111111111-111-1-1-1-1-1-111111111111111-11111-1-1-1-1-11111111111-1-1-11-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ9111111111-1-11−1−i32−1+i321111−1−i32−1+i32111-11-1-1-1-1−1−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+i321111111+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-11-11-1−1−i32−1+i32111+i321−i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321-1-11−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321−i32
χ10111111111-1-11−1−i32−1+i321111−1−i32−1+i32-111-1-1-1-1-1-1−1−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+i32-11111-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-11-111+i321−i32111+i321−i321+i321−i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-11+i321−i321+i321−i3211−1−i32−1+i32−1−i32−1+i32
χ11111111111-1-11−1+i32−1−i321111−1+i32−1−i32111-11-1-1-1-1−1+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−i321111111−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-11-11-1−1+i32−1−i32111−i321+i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321-1-11−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321+i32
χ12111111111-1-11−1+i32−1−i321111−1+i32−1−i32-111-1-1-1-1-1-1−1+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−i32-11111-11−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-11-111−i321+i32111−i321+i321−i321+i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-11−i321+i321−i321+i3211−1+i32−1−i32−1+i32−1−i32
χ1311-111-1-11111111-1-1-111111-1-1-111-1-11111-1-1-1-1-1-1111111-11-1-1111111-1-11-1-11-1-11-1-1-111111-1-1-1-1-111-1-111-1-1-11-1111-1-11-1-1-111
χ1411-111-1-11111111-1-1-1111-11-1-1111-1-11111-1-1-1-1-1-11111-11-11-11111111-1-11-1-11-1-11-111-1-1-1-11-1-1-11111-1-111-1-111-1-1-1-111-1111-1-1
χ1511-111-1-111111−1−i32−1+i32-1-1-11−1−i32−1+i3211-1-1-111-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i3211-11-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i32−1−i321+i321+i32−1+i321−i321−i321-1-1-111−1−i32−1+i321-11+i321−i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-11-11−1−i32−1+i321+i321−i321-11+i321−i32−1−i32−1+i32
χ1611-111-1-111111−1−i32−1+i32-1-1-11−1−i32−1+i32-11-1-1111-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-11-11-11−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i32−1−i321+i321+i32−1+i321−i321−i321-111-1-11+i321−i321-11+i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211-1-11+i321−i32−1−i32−1+i32-11−1−i32−1+i321+i321−i32
χ1711-111-1-111111−1+i32−1−i32-1-1-11−1+i32−1−i3211-1-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i3211-11-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i32−1+i321−i321−i32−1−i321+i321+i321-1-1-111−1+i32−1−i321-11−i321+i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-11-11−1+i32−1−i321−i321+i321-11−i321+i32−1+i32−1−i32
χ1811-111-1-111111−1+i32−1−i32-1-1-11−1+i32−1−i32-11-1-1111-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-11-11-11−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321+i32−1+i321−i321−i32−1−i321+i321+i321-111-1-11−i321+i321-11−i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211-1-11−i321+i32−1+i32−1−i32-11−1+i32−1−i321−i321+i32
χ1911-111-1-111-1-1111-1-1-111111-11-1-1-1111111-1-1-1-1-1-1111111-11-1-1-1-1-1-111-1-11-1-11-1-1-11-111-1111-111-1-1-1-111-1-111-1-11111-1-1-1111-1-1
χ2011-111-1-111-1-1111-1-1-1111-11-111-1-1111111-1-1-1-1-1-11111-11-11-11-1-1-1-111-1-11-1-11-1-1-111-1-11-1-11-11111-1-111-1-1111-11-1-1-1111-1-1-111
χ2111-111-1-111-1-11−1−i32−1+i32-1-1-11−1−i32−1+i3211-11-1-1-111−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i3211-11-1-11+i321+i321−i321−i32−1−i32−1+i321+i321−i32−1−i321+i321+i32−1+i321−i321−i32-11-111-1−1−i32−1+i321-1−1−i32−1+i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-111−1−i32−1+i321+i321−i32-11−1−i32−1+i321+i321−i32
χ2211-111-1-111-1-11−1−i32−1+i32-1-1-11−1−i32−1+i32-11-111-1-111−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i32-11-11-111+i321+i321−i321−i32−1−i32−1+i321+i321−i32−1−i321+i321+i32−1+i321−i321−i32-111-1-111+i321−i321-1−1−i32−1+i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-11-11+i321−i32−1−i32−1+i321-11+i321−i32−1−i32−1+i32
χ2311-111-1-111-1-11−1+i32−1−i32-1-1-11−1+i32−1−i3211-11-1-1-111−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i3211-11-1-11−i321−i321+i321+i32−1+i32−1−i321−i321+i32−1+i321−i321−i32−1−i321+i321+i32-11-111-1−1+i32−1−i321-1−1+i32−1−i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-111−1+i32−1−i321−i321+i32-11−1+i32−1−i321−i321+i32
χ2411-111-1-111-1-11−1+i32−1−i32-1-1-11−1+i32−1−i32-11-111-1-111−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1−i32-11-11-111−i321−i321+i321+i32−1+i32−1−i321−i321+i32−1+i321−i321−i32−1−i321+i321+i32-111-1-111−i321+i321-1−1+i32−1−i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-11-11−i321+i32−1+i32−1−i321-11−i321+i32−1+i32−1−i32
χ252222-1-1-1-1222-1222-1-1-12202220-1-1-1-1-1-12222-1-1-1-122-1-10-1-12202222-1-122-1-1-1-1-1-122000000-1-12200-1-1-1-1-1-1-1-10-1-100000000000
χ262222-1-1-1-1222-1−1−i3−1+i32-1-1-1−1−i3−1+i302220-1-1-1-11+i321−i32−1−i3−1+i3−1−i3−1+i31+i321+i321−i321−i32−1−i3−1+i31+i321−i320-1-1220−1−i3−1−i3−1+i3−1+i31+i321−i32−1−i3−1+i31+i321+i321+i321−i321−i321−i3222000000-1-1−1−i3−1+i3001+i321+i321+i321+i321−i321−i321−i321−i320-1-100000000000
χ272222-1-1-1-1222-1−1+i3−1−i32-1-1-1−1+i3−1−i302220-1-1-1-11−i321+i32−1+i3−1−i3−1+i3−1−i31−i321−i321+i321+i32−1+i3−1−i31−i321+i320-1-1220−1+i3−1+i3−1−i3−1−i31−i321+i32−1+i3−1−i31−i321−i321−i321+i321+i321+i3222000000-1-1−1+i3−1−i3001−i321−i321−i321−i321+i321+i321+i321+i320-1-100000000000
χ282222-1-1-1-12-2-2-1222-1-1-122022-201111-1-12222-1-1-1-122-1-10-1-1220-2-2-2-2-1-122-1-1-1-1-1-1-2-2000000-1-1-2-2001111111101100000000000
χ292222-1-1-1-12-2-2-1−1−i3−1+i32-1-1-1−1−i3−1+i3022-2011111+i321−i32−1−i3−1+i3−1−i3−1+i31+i321+i321−i321−i32−1−i3−1+i31+i321−i320-1-12201+i31+i31−i31−i31+i321−i32−1−i3−1+i31+i321+i321+i321−i321−i321−i32-2-2000000-1-11+i31−i300−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3201100000000000
χ302222-1-1-1-12-2-2-1−1+i3−1−i32-1-1-1−1+i3−1−i3022-2011111−i321+i32−1+i3−1−i3−1+i3−1−i31−i321−i321+i321+i32−1+i3−1−i31−i321+i320-1-12201−i31−i31+i31+i31−i321+i32−1+i3−1−i31−i321−i321−i321+i321+i321+i32-2-2000000-1-11−i31+i300−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3201100000000000
χ31222-12222-100-122-1-1-1-12222202000022-1-1222222-1-122-122-1-1-10000-1-1-1-1-1-1-1-1-1-100202022-1-1002200000000-100-1-1-1-1-1000000
χ32222-12222-100-122-1-1-1-122-2220-2000022-1-1222222-1-122122-1-110000-1-1-1-1-1-1-1-1-1-100-20-20-2-2-1-100-2-20000000010011111000000
χ33222-12222-100-1−1−i3−1+i3-1-1-1-1−1−i3−1+i3222020000−1−i3−1+i31+i321−i32−1−i3−1+i3−1−i3−1−i3−1+i3−1+i31+i321−i32−1−i3−1+i3-122-1-1-100001+i321−i321+i321−i321+i321+i321+i321−i321−i321−i32002020−1−i3−1+i3-1-100−1−i3−1+i300000000-100-11+i321−i321+i321−i32000000
χ34222-12222-100-1−1−i3−1+i3-1-1-1-1−1−i3−1+i3-2220-20000−1−i3−1+i31+i321−i32−1−i3−1+i3−1−i3−1−i3−1+i3−1+i31+i321−i32−1−i3−1+i3122-1-1100001+i321−i321+i321−i321+i321+i321+i321−i321−i321−i3200-20-201+i31−i3-1-1001+i31−i3000000001001−1−i32−1+i32−1−i32−1+i32000000
χ35222-12222-100-1−1+i3−1−i3-1-1-1-1−1+i3−1−i3222020000−1+i3−1−i31−i321+i32−1+i3−1−i3−1+i3−1+i3−1−i3−1−i31−i321+i32−1+i3−1−i3-122-1-1-100001−i321+i321−i321+i321−i321−i321−i321+i321+i321+i32002020−1+i3−1−i3-1-100−1+i3−1−i300000000-100-11−i321+i321−i321+i32000000
χ36222-12222-100-1−1+i3−1−i3-1-1-1-1−1+i3−1−i3-2220-20000−1+i3−1−i31−i321+i32−1+i3−1−i3−1+i3−1+i3−1−i3−1−i31−i321+i32−1+i3−1−i3122-1-1100001−i321+i321−i321+i321−i321−i321−i321+i321+i321+i3200-20-201−i31+i3-1-1001−i31+i3000000001001−1+i32−1−i32−1+i32−1−i32000000
χ3722-22-111-1222-122-211-12202-2-20-1-111-1-122-2-2111122-1-10-112-202222-1-1-2-2-111-1112-2000000-11-2-200-1-111-1-1110-1100000000000
χ3822-22-111-1222-1−1−i3−1+i3-211-1−1−i3−1+i302-2-20-1-1111+i321−i32−1−i3−1+i31+i31−i3−1−i32−1−i32−1+i32−1+i32−1−i3−1+i31+i321−i320-112-20−1−i3−1−i3−1+i3−1+i31+i321−i321+i31−i31+i32−1−i32−1−i321−i32−1+i32−1+i322-2000000-111+i31−i3001+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i320-1100000000000
χ3922-22-111-1222-1−1+i3−1−i3-211-1−1+i3−1−i302-2-20-1-1111−i321+i32−1+i3−1−i31−i31+i3−1+i32−1+i32−1−i32−1−i32−1+i3−1−i31−i321+i320-112-20−1+i3−1+i3−1−i3−1−i31−i321+i321−i31+i31−i32−1+i32−1+i321+i32−1−i32−1−i322-2000000-111−i31+i3001−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i320-1100000000000
χ4022-22-111-12-2-2-122-211-12202-22011-1-1-1-122-2-2111122-1-10-112-20-2-2-2-2-1-1-2-2-111-111-22000000-11220011-1-111-1-101-100000000000
χ4122-22-111-12-2-2-1−1−i3−1+i3-211-1−1−i3−1+i302-22011-1-11+i321−i32−1−i3−1+i31+i31−i3−1−i32−1−i32−1+i32−1+i32−1−i3−1+i31+i321−i320-112-201+i31+i31−i31−i31+i321−i321+i31−i31+i32−1−i32−1−i321−i32−1+i32−1+i32-22000000-11−1−i3−1+i300−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3201-100000000000
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χ4322-2-12-2-22-100-122111-12222-20-2000022-1-1-2-2-2-2-2-2-1-122-12-2-1110000-1-111-111-11100-202022-1100-2-200000000100-1-1-111000000
χ4422-2-12-2-22-100-122111-122-22-202000022-1-1-2-2-2-2-2-2-1-12212-2-11-10000-1-111-111-1110020-20-2-2-11002200000000-100111-1-1000000
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χ4622-2-12-2-22-100-1−1−i3−1+i3111-1−1−i3−1+i3-22-2020000−1−i3−1+i31+i321−i321+i31−i31+i31+i31−i31−i31+i321−i32−1−i3−1+i312-2-11-100001+i321−i32−1−i32−1+i321+i32−1−i32−1−i321−i32−1+i32−1+i320020-201+i31−i3-1100−1−i3−1+i300000000-1001−1−i32−1+i321+i321−i32000000
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χ4822-2-12-2-22-100-1−1+i3−1−i3111-1−1+i3−1−i3-22-2020000−1+i3−1−i31−i321+i321−i31+i31−i31−i31+i31+i31−i321+i32−1+i3−1−i312-2-11-100001−i321+i32−1+i32−1−i321−i32−1+i32−1+i321+i32−1−i32−1−i320020-201−i31+i3-1100−1+i3−1−i300000000-1001−1+i32−1−i321−i321+i32000000
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χ57444-2-2-2-2-2-200144-211144044000000-2-2-2-244-2-2-2-2-2-2-2-20-2-2-2-20000011-2-2111111000000001100000000000000000000000000
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χ6044-4-2-222-2-2001442-1-114404-4000000-2-2-2-2-4-42222-2-2-2-20-22-220000011221-1-11-1-1000000001-100000000000000000000000000
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χ991212-12-6-666-6-6003006-3-33000-440000000000000000000002-22-200000000000000000000000-1100000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.