Finite Group Databasebeta

← Group #72228955

Character table — Group #72228955

Order 3888.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size112222244444466669999121212121212121212121212121212121212121212121818181818181818181818181818363636363636363636363636363636365454545454545454818181818181108108108108108108108108108108108108162162162
order122336636666699181833669999918181818181818181818181818181818182244669999181818186699121218181818181818181818666612121212226666181818181818363636363636266
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-11-111111111111-1111-1111111111111-1-111-1-1-1-1-1-1-1-11-111-1-11-111-1-1-1-1-1
χ31111111111111111111111111111111111111111111-11-111111111111-1111-111111111111-1-111-1-111-1-1-1-1-1-1-11-1-111-11-1-111-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-11111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111
χ511111111111111111−1+i32−1−i32−1+i32−1−i3211111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+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−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32
χ611111111111111111−1+i32−1−i32−1+i32−1−i3211111111111111111111111-11-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321-1−1+i32−1−i321-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i321-1−1+i32−1−i321−i321+i321-1−1+i32−1−i321−i321+i32-11−i321+i32
χ711111111111111111−1+i32−1−i32−1+i32−1−i321111111111111111111111-11-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-11−1+i32−1−i32-11−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321+i32−1+i32−1−i321−i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i32-111−i321+i32−1+i32−1−i32-111−i321+i32−1+i32−1−i32-11−i321+i32
χ811111111111111111−1+i32−1−i32−1+i32−1−i321111111111111111111111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1−1+i32−1−i32-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321+i321−i321+i321−i321+i321−i321+i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321+i321−i321+i32-1-11−i321+i321−i321+i321−1+i32−1−i32
χ911111111111111111−1−i32−1+i32−1−i32−1+i3211111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−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+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32
χ1011111111111111111−1−i32−1+i32−1−i32−1+i3211111111111111111111111-11-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321-1−1−i32−1+i321-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i321-1−1−i32−1+i321+i321−i321-1−1−i32−1+i321+i321−i32-11+i321−i32
χ1111111111111111111−1−i32−1+i32−1−i32−1+i321111111111111111111111-11-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-11−1−i32−1+i32-11−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i32-111+i321−i32−1−i32−1+i32-111+i321−i32−1−i32−1+i32-11+i321−i32
χ1211111111111111111−1−i32−1+i32−1−i32−1+i321111111111111111111111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1−1−i32−1+i32-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321−i321+i321−i32-1-11+i321−i321+i321−i321−1−i32−1+i32
χ1311-111111-1-11-1-11111111111111-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-11-1-11-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1
χ1411-111111-1-11-1-11111111111111-1-111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1111111111-111-11-1-1-1-11-1-11-1-111-1-1-1-111-1-1-1-1-1-11-111-1-1-11-1-111111
χ1511-111111-1-11-1-11111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-111-1-1-111111111-11111-1-1-1-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1111-111-1-1111
χ1611-111111-1-11-1-11111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-11111-1-1-1-11-1-11-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1
χ1711-111111-1-11-1-11111−1+i32−1−i32−1+i32−1−i3211111-1-111111-1-1-1-1-1-1-1-1-1-111-1-11−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32-1-11−i321−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321+i32-11−i321+i32
χ1811-111111-1-11-1-11111−1+i32−1−i32−1+i32−1−i3211111-1-111111-1-1-1-1-1-1-1-1-1-11-1-111−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321-1−1+i32−1−i32-111−i321−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32-1-11−i321−i321+i321+i321-1−1+i32−1−i321−i321+i32-111−i321+i32−1+i32−1−i321−1+i32−1−i32
χ1911-111111-1-11-1-11111−1+i32−1−i32−1+i32−1−i3211111-1-111111-1-1-1-1-1-1-1-1-1-1-111-11−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-11−1+i32−1−i321-11−i321−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i32-1-11−i321−i321+i321+i32-111−i321+i32−1+i32−1−i321-1−1+i32−1−i321−i321+i321−1+i32−1−i32
χ2011-111111-1-11-1-11111−1+i32−1−i32−1+i32−1−i3211111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1−1+i32−1−i32111−i321−i321+i321+i32−1+i321−i321−i32−1−i321+i321+i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321+i321−i321+i3211−1+i32−1−i32−1+i32−1−i32-11−i321+i32
χ2111-111111-1-11-1-11111−1−i32−1+i32−1−i32−1+i3211111-1-111111-1-1-1-1-1-1-1-1-1-111-1-11+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32-1-11+i321+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321−i32-11+i321−i32
χ2211-111111-1-11-1-11111−1−i32−1+i32−1−i32−1+i3211111-1-111111-1-1-1-1-1-1-1-1-1-11-1-111+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321-1−1−i32−1+i32-111+i321+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32-1-11+i321+i321−i321−i321-1−1−i32−1+i321+i321−i32-111+i321−i32−1−i32−1+i321−1−i32−1+i32
χ2311-111111-1-11-1-11111−1−i32−1+i32−1−i32−1+i3211111-1-111111-1-1-1-1-1-1-1-1-1-1-111-11+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-11−1−i32−1+i321-11+i321+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32-1-11+i321+i321−i321−i32-111+i321−i32−1−i32−1+i321-1−1−i32−1+i321+i321−i321−1−i32−1+i32
χ2411-111111-1-11-1-11111−1−i32−1+i32−1−i32−1+i3211111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1−1−i32−1+i32111+i321+i321−i321−i32−1−i321+i321+i32−1+i321−i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321−i321+i321−i3211−1−i32−1+i32−1−i32−1+i32-11+i321−i32
χ2522222222222222-12-122222-1-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-10202222-12-12-12-102-1-1022-12-1-1-1-1-1-1-1002200220000000-100-1-10-100-1-1000
χ2622222222222222-12-122222-1-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-10-20-2222-12-12-12-10-2-1-10-22-12-1-1-1-1-1-1-100-2-200-2-2000000010011010011000
χ2722222222222222-12-1−1+i3−1−i3−1+i3−1−i32-1-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-10202−1+i3−1−i3−1+i31−i32−1−i31+i32−1+i31−i32−1−i31+i32021−i321+i3202−1+i31−i32−1−i31+i321−i321−i321−i321+i321+i321+i3200−1+i3−1−i300−1+i3−1−i30000000-1001−i321+i320-1001−i321+i32000
χ2822222222222222-12-1−1+i3−1−i3−1+i3−1−i32-1-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-10-20-2−1+i3−1−i3−1+i31−i32−1−i31+i32−1+i31−i32−1−i31+i320-21−i321+i320-2−1+i31−i32−1−i31+i321−i321−i321−i321+i321+i321+i32001−i31+i3001−i31+i30000000100−1+i32−1−i320100−1+i32−1−i32000
χ2922222222222222-12-1−1−i3−1+i3−1−i3−1+i32-1-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-10202−1−i3−1+i3−1−i31+i32−1+i31−i32−1−i31+i32−1+i31−i32021+i321−i3202−1−i31+i32−1+i31−i321+i321+i321+i321−i321−i321−i3200−1−i3−1+i300−1−i3−1+i30000000-1001+i321−i320-1001+i321−i32000
χ3022222222222222-12-1−1−i3−1+i3−1−i3−1+i32-1-1-1-12-12-1-1-1-122-1-1-1-1-1-1-1-10-20-2−1−i3−1+i3−1−i31+i32−1+i31−i32−1−i31+i32−1+i31−i320-21+i321−i320-2−1−i31+i32−1+i31−i321+i321+i321+i321−i321−i321−i32001+i31−i3001+i31−i30000000100−1−i32−1+i320100−1−i32−1+i32000
χ312222222222222-12-122222-12-1-1-1-12-12-1-1-1-1-122-1-1-1-1-1-1202022-12-12-12-1220-1-120-12-12-1-1-1-1-1-122002200000000-10-1-100-10-1-100000
χ322222222222222-12-122222-12-1-1-1-12-12-1-1-1-1-122-1-1-1-1-1-1-20-2022-12-12-12-12-20-1-1-20-12-12-1-1-1-1-1-1-2-200-2-200000000101100101100000
χ332222222222222-12-12−1+i3−1−i3−1+i3−1−i3-12-1-1-1-12-12-1-1-1-1-122-1-1-1-1-1-12020−1+i3−1−i31−i32−1+i31+i32−1−i31−i32−1+i31+i32−1−i3201−i321+i32201−i32−1+i31+i32−1−i31−i321−i321−i321+i321+i321+i32−1+i3−1−i300−1+i3−1−i300000000-101−i321+i3200-101−i321+i3200000
χ342222222222222-12-12−1+i3−1−i3−1+i3−1−i3-12-1-1-1-12-12-1-1-1-1-122-1-1-1-1-1-1-20-20−1+i3−1−i31−i32−1+i31+i32−1−i31−i32−1+i31+i32−1−i3-201−i321+i32-201−i32−1+i31+i32−1−i31−i321−i321−i321+i321+i321+i321−i31+i3001−i31+i30000000010−1+i32−1−i320010−1+i32−1−i3200000
χ352222222222222-12-12−1−i3−1+i3−1−i3−1+i3-12-1-1-1-12-12-1-1-1-1-122-1-1-1-1-1-12020−1−i3−1+i31+i32−1−i31−i32−1+i31+i32−1−i31−i32−1+i3201+i321−i32201+i32−1−i31−i32−1+i31+i321+i321+i321−i321−i321−i32−1−i3−1+i300−1−i3−1+i300000000-101+i321−i3200-101+i321−i3200000
χ362222222222222-12-12−1−i3−1+i3−1−i3−1+i3-12-1-1-1-12-12-1-1-1-1-122-1-1-1-1-1-1-20-20−1−i3−1+i31+i32−1−i31−i32−1+i31+i32−1−i31−i32−1+i3-201+i321−i32-201+i32−1−i31−i32−1+i31+i321+i321+i321−i321−i321−i321+i31−i3001+i31−i30000000010−1−i32−1+i320010−1−i32−1+i3200000
χ3722-222222-2-22-2-22-12-122222-1-1-1-1-212-1-1-1-1-2-211111111020-2-2-22-12-12-12-102-1-10-2-21-21-111-111002200-2-20000000-100-1-1010011000
χ3822-222222-2-22-2-22-12-122222-1-1-1-1-212-1-1-1-1-2-2111111110-202-2-22-12-12-12-10-2-1-102-21-21-111-11100-2-200220000000100110-100-1-1000
χ3922-222222-2-22-2-22-12-1−1+i3−1−i3−1+i3−1−i32-1-1-1-1-212-1-1-1-1-2-211111111020-21−i31+i3−1+i31−i32−1−i31+i32−1+i31−i32−1−i31+i32021−i321+i320-21−i3−1+i321+i3−1−i321−i32−1+i32−1+i321+i32−1−i32−1−i3200−1+i3−1−i3001−i31+i30000000-1001−i321+i320100−1+i32−1−i32000
χ4022-222222-2-22-2-22-12-1−1+i3−1−i3−1+i3−1−i32-1-1-1-1-212-1-1-1-1-2-2111111110-2021−i31+i3−1+i31−i32−1−i31+i32−1+i31−i32−1−i31+i320-21−i321+i32021−i3−1+i321+i3−1−i321−i32−1+i32−1+i321+i32−1−i32−1−i32001−i31+i300−1+i3−1−i30000000100−1+i32−1−i320-1001−i321+i32000
χ4122-222222-2-22-2-22-12-1−1−i3−1+i3−1−i3−1+i32-1-1-1-1-212-1-1-1-1-2-211111111020-21+i31−i3−1−i31+i32−1+i31−i32−1−i31+i32−1+i31−i32021+i321−i320-21+i3−1−i321−i3−1+i321+i32−1−i32−1−i321−i32−1+i32−1+i3200−1−i3−1+i3001+i31−i30000000-1001+i321−i320100−1−i32−1+i32000
χ4222-222222-2-22-2-22-12-1−1−i3−1+i3−1−i3−1+i32-1-1-1-1-212-1-1-1-1-2-2111111110-2021+i31−i3−1−i31+i32−1+i31−i32−1−i31+i32−1+i31−i320-21+i321−i32021+i3−1−i321−i3−1+i321+i32−1−i32−1−i321−i32−1+i32−1+i32001+i31−i300−1−i3−1+i30000000100−1−i32−1+i320-1001+i321−i32000
χ4322-222222-2-22-2-2-12-122222-12-1-1-11-2-12-1-1-111-2-211111120-20-2-2-12-12-12-1220-1-1-201-21-2-111-1112200-2-200000000-10-1-100101100000
χ4422-222222-2-22-2-2-12-122222-12-1-1-11-2-12-1-1-111-2-2111111-2020-2-2-12-12-12-12-20-1-1201-21-2-111-111-2-2002200000000101100-10-1-100000
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Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.