Finite Group Databasebeta

← Group #13144765

Character table — Group #13144765

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113
size111111111111222222444444444444666666666666666688812121212121212121212121212121212121212121212121218181818181824242424242424242424242424242424363636363636363636363636363636727272
order12223366666644121212124488121212122424242433336666666666664121212121212121212122424242424242424242424242424242422666612121212121212121212121212121212444881212121212122424242441212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-11111-1-1-1-11111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-1
χ411111111111111111111-1-11111-1-1-1-11111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111
χ5111111111111111111-1-111-1-1-1-111111111111111111111-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1
χ6111111111111111111-1-111-1-1-1-111111111111111111111-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1111
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1-111111111-1-1-1
χ92222222222222222222222222222222-1-1-122-1-1-1-1-1-12-1-1-12222-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000
χ10222222222222222222222222222222-12-1-1-1-122-1-1-1-1-12-1-1222-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000
χ11222222222222222222222222222222-1-12-1-1-1-1-122-1-1-1-12-1222-1-12-1-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-1000000-1-1-1-122-1-1-1-1-1-122-1-1000000000000000000
χ12222222222222222222222222222222-1-1-12-1-1-1-1-1-122-1-1-12222-1-1-12-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222000000-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000
χ1322222222222222222222-2-22222-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-1-2-2-22-1-1-12-1-1-1-2-2-2-211111111111100000022-1-1-1-1-1-1-2-2111111000000000000000000
χ1422222222222222222222-2-22222-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-1-2-2-2-12-1-1-12-1-11111-2-2-2-211111111000000-1-122-1-1-1-111-2-21111000000000000000000
χ1522222222222222222222-2-22222-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-1-2-2-2-1-12-1-1-12-111111111-2-2-2-21111000000-1-1-1-122-1-11111-2-211000000000000000000
χ1622222222222222222222-2-22222-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12-2-2-2-1-1-12-1-1-12111111111111-2-2-2-2000000-1-1-1-1-1-122111111-2-2000000000000000000
χ17222222222222222222-2-222-2-2-2-222222-1-1-122-1-1-1-1-1-12-1-1-1-2-2-22-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000-2-2111111-2-2111111000000000000000000
χ18222222222222222222-2-222-2-2-2-22222-12-1-1-1-122-1-1-1-1-12-1-1-2-2-2-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000011-2-2111111-2-21111000000000000000000
χ19222222222222222222-2-222-2-2-2-22222-1-12-1-1-1-1-122-1-1-1-12-1-2-2-2-1-12-1-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-10000001111-2-2111111-2-211000000000000000000
χ20222222222222222222-2-222-2-2-2-22222-1-1-12-1-1-1-1-1-122-1-1-12-2-2-2-1-1-12-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222000000111111-2-2111111-2-2000000000000000000
χ21222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22-1-1-122-1-1-1-1-1-12-1-1-12222-1-1-12-1-1-1-2-2-2-2111111111111000000-2-211111122-1-1-1-1-1-1000000000000000000
χ22222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-12-1-1-1-122-1-1-1-1-12-1-1222-12-1-1-12-1-11111-2-2-2-21111111100000011-2-21111-1-122-1-1-1-1000000000000000000
χ23222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-1-12-1-1-1-1-122-1-1-1-12-1222-1-12-1-1-12-111111111-2-2-2-211110000001111-2-211-1-1-1-122-1-1000000000000000000
χ24222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-12-1-1-1-1-1-122-1-1-12222-1-1-12-1-1-12111111111111-2-2-2-2000000111111-2-2-1-1-1-1-1-122000000000000000000
χ25222222222222-2-2-2-2-2-20000000000002222222222222222000-2-2-2-2-2-2-2-200000000000000002222220000000000000000-20000-2-200000000000
χ26222222222222-2-2-2-2-2-20000000000002222222222222222000-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-20000000000000000200002200000000000
χ2722-2-22222-2-2-2-2000000002−2000022−2−222222-22-22-22-2-2-2-2-20000000000022−2−222−2−222−2−222−2−22-222-2-200000000000000000002−200000022−2−2000
χ2822-2-22222-2-2-2-2000000002−2000022−2−222222-22-22-22-2-2-2-2-20000000000022−2−222−2−222−2−222−2−2-22-2-2220000000000000000000−22000000−2−222000
χ2922-2-22222-2-2-2-200000000−220000−2−22222222-22-22-22-2-2-2-2-200000000000−2−222−2−222−2−222−2−2222-222-2-20000000000000000000−22000000−2−222000
χ3022-2-22222-2-2-2-200000000−220000−2−22222222-22-22-22-2-2-2-2-200000000000−2−222−2−222−2−222−2−222-22-2-22200000000000000000002−200000022−2−2000
χ312-2-2222-2-2-2-2222-222-2-22-20022-2-200002222-2-2-2-2-2-2-2-22222000-2-2-2-2222200000000000000000000002-22-22-22-200000000000000000000000000
χ322-2-2222-2-2-2-2222-222-2-22-20022-2-200002-1-1-1-2-21111112-1-1-1000-21112-1-1-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000002-2-11-11-1100−i3i3−i3i3−i3i3000000000000000000
χ332-2-2222-2-2-2-2222-222-2-22-20022-2-200002-1-1-1-2-21111112-1-1-1000-21112-1-1-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000002-2-11-11-1100i3−i3i3−i3i3−i3000000000000000000
χ342-2-2222-2-2-2-2222-222-2-22-20022-2-20000-12-1-111-2-21111-12-1-10001-211-12-1-1−i3i3−i3i30000−i3i3−i3i3i3−i3i3−i3000000-112-2-11-11−i3i300−i3i3i3−i3000000000000000000
χ352-2-2222-2-2-2-2222-222-2-22-20022-2-20000-12-1-111-2-21111-12-1-10001-211-12-1-1i3−i3i3−i30000i3−i3i3−i3−i3i3−i3i3000000-112-2-11-11i3−i300i3−i3−i3i3000000000000000000
χ362-2-2222-2-2-2-2222-222-2-22-20022-2-20000-1-12-11111-2-211-1-12-100011-21-1-12-1−i3i3−i3i3i3−i3i3−i30000−i3i3−i3i3000000-11-112-2-11−i3i3i3−i300−i3i3000000000000000000
χ372-2-2222-2-2-2-2222-222-2-22-20022-2-20000-1-12-11111-2-211-1-12-100011-21-1-12-1i3−i3i3−i3−i3i3−i3i30000i3−i3i3−i3000000-11-112-2-11i3−i3−i3i300i3−i3000000000000000000
χ382-2-2222-2-2-2-2222-222-2-22-20022-2-20000-1-1-12111111-2-2-1-1-12000111-2-1-1-12−i3i3−i3i3−i3i3−i3i3i3−i3i3−i30000000000-11-11-112-2−i3i3−i3i3i3−i300000000000000000000
χ392-2-2222-2-2-2-2222-222-2-22-20022-2-20000-1-1-12111111-2-2-1-1-12000111-2-1-1-12i3−i3i3−i3i3−i3i3−i3−i3i3−i3i30000000000-11-11-112-2i3−i3i3−i3−i3i300000000000000000000
χ402-2-2222-2-2-2-2222-222-2-2-2200-2-22200002222-2-2-2-2-2-2-2-22222000-2-2-2-222220000000000000000000000-22-22-22-2200000000000000000000000000
χ412-2-2222-2-2-2-2222-222-2-2-2200-2-22200002-1-1-1-2-21111112-1-1-1000-21112-1-1-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000-221-11-11-100i3−i3i3−i3i3−i3000000000000000000
χ422-2-2222-2-2-2-2222-222-2-2-2200-2-22200002-1-1-1-2-21111112-1-1-1000-21112-1-1-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000-221-11-11-100−i3i3−i3i3−i3i3000000000000000000
χ432-2-2222-2-2-2-2222-222-2-2-2200-2-2220000-12-1-111-2-21111-12-1-10001-211-12-1-1−i3i3−i3i30000−i3i3−i3i3i3−i3i3−i30000001-1-221-11-1i3−i300i3−i3−i3i3000000000000000000
χ442-2-2222-2-2-2-2222-222-2-2-2200-2-2220000-12-1-111-2-21111-12-1-10001-211-12-1-1i3−i3i3−i30000i3−i3i3−i3−i3i3−i3i30000001-1-221-11-1−i3i300−i3i3i3−i3000000000000000000
χ452-2-2222-2-2-2-2222-222-2-2-2200-2-2220000-1-12-11111-2-211-1-12-100011-21-1-12-1−i3i3−i3i3i3−i3i3−i30000−i3i3−i3i30000001-11-1-221-1i3−i3−i3i300i3−i3000000000000000000
χ462-2-2222-2-2-2-2222-222-2-2-2200-2-2220000-1-12-11111-2-211-1-12-100011-21-1-12-1i3−i3i3−i3−i3i3−i3i30000i3−i3i3−i30000001-11-1-221-1−i3i3i3−i300−i3i3000000000000000000
χ472-2-2222-2-2-2-2222-222-2-2-2200-2-2220000-1-1-12111111-2-2-1-1-12000111-2-1-1-12−i3i3−i3i3−i3i3−i3i3i3−i3i3−i300000000001-11-11-1-22i3−i3i3−i3−i3i300000000000000000000
χ482-2-2222-2-2-2-2222-222-2-2-2200-2-2220000-1-1-12111111-2-2-1-1-12000111-2-1-1-12i3−i3i3−i3i3−i3i3−i3−i3i3−i3i300000000001-11-11-1-22−i3i3−i3i3i3−i300000000000000000000
χ492-2-2222-2-2-2-222-22-2-2220000000000002222-2-2-2-2-2-2-2-222220002222-2-2-2-20000000000000000000000000000000000000002-2000022-2-20000000
χ502-2-2222-2-2-2-222-22-2-2220000000000002222-2-2-2-2-2-2-2-222220002222-2-2-2-2000000000000000000000000000000000000000-220000-2-2220000000
χ513333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3200000000000000003−3−3i32−3+3i3200000000000000000000000011−1−i32−1+i32−1−i32−1+i32000000000000000011111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32
χ523333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3200000000000000003−3−3i32−3+3i32000000000000000000000000-1-11+i321−i321+i321−i320000000000000000-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32-11+i321−i32
χ533333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i320000000000000000-33+3i323−3i3200000000000000000000000011−1−i32−1+i32−1−i32−1+i320000000000000000111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32-11+i321−i32
χ543333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i320000000000000000-33+3i323−3i32000000000000000000000000-1-11+i321−i321+i321−i320000000000000000-1-1-1111+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32
χ553333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-3333+3i323−3i323+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i320000000000000000-33+3i323−3i3200000000000000000000000011−1−i32−1+i32−1−i32−1+i3200000000000000001-1-111−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32-11+i321−i32
χ563333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-3333+3i323−3i323+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i320000000000000000-33+3i323−3i32000000000000000000000000-1-11+i321−i321+i321−i320000000000000000-111-1-11+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321−1−i32−1+i32
χ573333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-3-3-33+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i3200000000000000003−3−3i32−3+3i3200000000000000000000000011−1−i32−1+i32−1−i32−1+i3200000000000000001-1-1-1-1−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i321−1−i32−1+i32
χ583333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-3-3-33+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i3200000000000000003−3−3i32−3+3i32000000000000000000000000-1-11+i321−i321+i321−i320000000000000000-111111+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11+i321−i32
χ593333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i323333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3200000000000000003−3+3i32−3−3i3200000000000000000000000011−1+i32−1−i32−1+i32−1−i32000000000000000011111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32
χ603333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i323333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3200000000000000003−3+3i32−3−3i32000000000000000000000000-1-11−i321+i321−i321+i320000000000000000-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321−i321+i32-11−i321+i32
χ613333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3233-3-3−3+3i32−3−3i32−3+3i32−3−3i323−3i323+3i323−3i323+3i320000000000000000-33−3i323+3i3200000000000000000000000011−1+i32−1−i32−1+i32−1−i320000000000000000111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32-11−i321+i32
χ623333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3233-3-3−3+3i32−3−3i32−3+3i32−3−3i323−3i323+3i323−3i323+3i320000000000000000-33−3i323+3i32000000000000000000000000-1-11−i321+i321−i321+i320000000000000000-1-1-1111−i321+i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32
χ633333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-3-3333−3i323+3i323−3i323+3i32−3+3i32−3−3i32−3+3i32−3−3i320000000000000000-33−3i323+3i3200000000000000000000000011−1+i32−1−i32−1+i32−1−i3200000000000000001-1-111−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32-11−i321+i32
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χ9666-6-6−3−3i3−3+3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i30000000032−320000−3ζ7+3ζ133ζ5−3ζ233ζ7−3ζ13−3ζ5+3ζ2300000000000000000000000000000000000000000002-2−1−i3−1+i31+i31−i300000000000000000002−2000000−ζ7+ζ13ζ5−ζ23ζ7−ζ13−ζ5+ζ23000
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χ1066-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i3-663+3i33−3i3−3−3i3−3+3i30000000000000000000000000000000000000000000000000000000000000000000000000000002-20000−1−i3−1+i31+i31−i30000000
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χ1096-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i36-6−3+3i3−3−3i33−3i33+3i3-66003−3i33+3i3−3+3i3−3−3i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1106-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i3-663−3i33+3i3−3+3i3−3−3i30000000000000000000000000000000000000000000000000000000000000000000000000000002-20000−1+i3−1−i31−i31+i30000000
χ1116-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i3-663−3i33+3i3−3+3i3−3−3i3000000000000000000000000000000000000000000000000000000000000000000000000000000-2200001−i31+i3−1+i3−1−i30000000
χ11212-1212-12−6−6i3−6+6i36+6i36−6i3−6−6i3−6+6i36+6i36−6i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11312-1212-12−6+6i3−6−6i36−6i36+6i3−6+6i3−6−6i36−6i36+6i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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