Finite Group Databasebeta

← Group #13173411

Character table — Group #13173411

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1122222224444444444444444444444444444444488888888888888888888888888888888888899181818181818183636363636363636108108108108108108108108
order1223446662233333366666666666666666666661212666666666666666666666666121212121212121212121212442241212121244661212121244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ411111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ5111111111-1-1111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-111-1-1-1-11111-1-1-1-1
χ6111111111-1-1111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-111-1-1-1-1-1-1-1-11111
χ7111111111-1-1111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-11111ii−i−i−i−iii
χ8111111111-1-1111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-11111−i−iiiii−i−i
χ911-111-1-1-111-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-11-111-1-11-11-111-1-11-11-11-11-1
χ1011-111-1-1-111-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-11-111-1-11-11-111-1-1-11-11-11-11
χ1111-111-1-1-111-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-11-1-111-11-11-1-111i−i−iii−i−ii
χ1211-111-1-1-111-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-11-1-111-11-11-1-111−iii−i−iii−i
χ1311-111-1-1-11-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-111-11-111-1-1-111-1-1-1111-11-1-11-11
χ1411-111-1-1-11-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-111-11-111-1-1-111-1-1-111-11-111-11-1
χ1511-111-1-1-11-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11-11-1-1111-1-1111-1-1i−i−ii−iii−i
χ1611-111-1-1-11-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11-11-1-1111-1-1111-1-1−iii−ii−i−ii
χ172222-2-2222002222220000222222222222222222-2-2000000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-222-2-22222200-2-2000000000000
χ182222-2-2222002222220000222222222222222222-2-2000000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-20022000000000000
χ19222-122-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122222-1-1-1-122-1-1-1-1-1-100000000
χ20222-122-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-2-21111-2-211111100000000
χ21222-122-1-1-1-2-222-1-1-1-111112222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111-2-2-2-21111111122-1-1-1-122-1-1-1-122222-1-1-1-1-2-2-1-1111100000000
χ22222-122-1-1-1-2-222-1-1-1-111112222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-211111111-2-2-2-21111111122-1-1-1-122-1-1-1-1-2-2-2-2-211112211-1-1-1-100000000
χ23222-1-2-2-1-1-10022-1-1-1-1−i3i3−i3i32222-1-1-1-1-1-1-1-122-1-1-1-1110000−i3−i3−i3−i3i3i3i3i30000−i3−i3−i3−i3i3i3i3i3-2-21111-2-2111122-2-22-1-1-1-10011−i3i3−i3i300000000
χ24222-1-2-2-1-1-10022-1-1-1-1−i3i3−i3i32222-1-1-1-1-1-1-1-122-1-1-1-1110000−i3−i3−i3−i3i3i3i3i30000−i3−i3−i3−i3i3i3i3i3-2-21111-2-21111-2-222-2111100-1-1i3−i3i3−i300000000
χ25222-1-2-2-1-1-10022-1-1-1-1i3−i3i3−i32222-1-1-1-1-1-1-1-122-1-1-1-1110000i3i3i3i3−i3−i3−i3−i30000i3i3i3i3−i3−i3−i3−i3-2-21111-2-2111122-2-22-1-1-1-10011i3−i3i3−i300000000
χ26222-1-2-2-1-1-10022-1-1-1-1i3−i3i3−i32222-1-1-1-1-1-1-1-122-1-1-1-1110000i3i3i3i3−i3−i3−i3−i30000i3i3i3i3−i3−i3−i3−i3-2-21111-2-21111-2-222-2111100-1-1−i3i3−i3i300000000
χ2722-22-22-2-22002222220000-2-2-2-2-2-2-2-2-2-2-2-2222222-22000000000000000000000000-2-2-2-2-2-2222222222-2-222-2-200-22000000000000
χ2822-22-22-2-22002222220000-2-2-2-2-2-2-2-2-2-2-2-2222222-22000000000000000000000000-2-2-2-2-2-2222222-2-2-222-2-222002-2000000000000
χ2922-2-12-211-12-222-1-1-1-1-1-111-2-2-2-21111111122-1-1-1-1-112222-1-1-1-1-1-1-1-1-2-2-2-21111111122-1-1-1-1-2-2111122-22-2-1-1112-2-11-1-11100000000
χ3022-2-12-211-12-222-1-1-1-1-1-111-2-2-2-21111111122-1-1-1-1-112222-1-1-1-1-1-1-1-1-2-2-2-21111111122-1-1-1-1-2-21111-2-22-2211-1-1-221-111-1-100000000
χ3122-2-12-211-1-2222-1-1-1-111-1-1-2-2-2-21111111122-1-1-1-1-11-2-2-2-2111111112222-1-1-1-1-1-1-1-122-1-1-1-1-2-2111122-22-2-1-111-22-1111-1-100000000
χ3222-2-12-211-1-2222-1-1-1-111-1-1-2-2-2-21111111122-1-1-1-1-11-2-2-2-2111111112222-1-1-1-1-1-1-1-122-1-1-1-1-2-21111-2-22-2211-1-12-21-1-1-11100000000
χ3322-2-1-2211-10022-1-1-1-1−i3i3i3−i3-2-2-2-21111111122-1-1-1-11-10000−i3−i3−i3−i3i3i3i3i30000i3i3i3i3−i3−i3−i3−i3-2-2111122-1-1-1-1222-2-2-1-111001-1−i3i3i3−i300000000
χ3422-2-1-2211-10022-1-1-1-1−i3i3i3−i3-2-2-2-21111111122-1-1-1-11-10000−i3−i3−i3−i3i3i3i3i30000i3i3i3i3−i3−i3−i3−i3-2-2111122-1-1-1-1-2-2-22211-1-100-11i3−i3−i3i300000000
χ3522-2-1-2211-10022-1-1-1-1i3−i3−i3i3-2-2-2-21111111122-1-1-1-11-10000i3i3i3i3−i3−i3−i3−i30000−i3−i3−i3−i3i3i3i3i3-2-2111122-1-1-1-1222-2-2-1-111001-1i3−i3−i3i300000000
χ3622-2-1-2211-10022-1-1-1-1i3−i3−i3i3-2-2-2-21111111122-1-1-1-11-10000i3i3i3i3−i3−i3−i3−i30000−i3−i3−i3−i3i3i3i3i3-2-2111122-1-1-1-1-2-2-22211-1-100-11−i3i3i3−i300000000
χ37444444444441-211-2-2444411-2-21111-2-2-2-21-211-2-24411-2-211-2-211-2-211-2-211-2-211-2-21-211-2-21-211-2-20000000000000000000000000
χ3844444444444-21-2-2114444-2-211-2-2-2-21111-21-2-21144-2-211-2-211-2-211-2-211-2-211-2-211-21-2-211-21-2-2110000000000000000000000000
χ39444444444-4-41-211-2-2-4-4-4-411-2-21111-2-2-2-21-211-2-244-1-122-1-122-1-122-1-122-1-122-1-1221-211-2-21-211-2-20000000000000000000000000
χ40444444444-4-4-21-2-211-4-4-4-4-2-211-2-2-2-21111-21-2-2114422-1-122-1-122-1-122-1-122-1-122-1-1-21-2-211-21-2-2110000000000000000000000000
χ414444-4-4444001-211-2-2000011-2-21111-2-2-2-21-211-2-2-4-43-3003-3003-3003-3003-3003-300-12-1-122-12-1-1220000000000000000000000000
χ424444-4-4444001-211-2-2000011-2-21111-2-2-2-21-211-2-2-4-4-3300-3300-3300-3300-3300-3300-12-1-122-12-1-1220000000000000000000000000
χ434444-4-444400-21-2-2110000-2-211-2-2-2-21111-21-2-211-4-4003-3003-3003-3003-3003-3003-32-122-1-12-122-1-10000000000000000000000000
χ444444-4-444400-21-2-2110000-2-211-2-2-2-21111-21-2-211-4-400-3300-3300-3300-3300-3300-332-122-1-12-122-1-10000000000000000000000000
χ45444-244-2-2-2441-2−1−3i32−1+3i3211-2-2-2-211-2-2−1−3i32−1−3i32−1+3i32−1+3i3211111-2−1−3i32−1+3i3211-2-211-2-2−1−3i32−1+3i3211−1+3i32−1−3i321111-2-2−1−3i32−1+3i3211−1+3i32−1−3i32111-2−1−3i32−1+3i32111-2−1−3i32−1+3i32110000000000000000000000000
χ46444-244-2-2-2441-2−1+3i32−1−3i3211-2-2-2-211-2-2−1+3i32−1+3i32−1−3i32−1−3i3211111-2−1+3i32−1−3i3211-2-211-2-2−1+3i32−1−3i3211−1−3i32−1+3i321111-2-2−1+3i32−1−3i3211−1−3i32−1+3i32111-2−1+3i32−1−3i32111-2−1+3i32−1−3i32110000000000000000000000000
χ47444-244-2-2-244-2111−1−3i32−1+3i32-2-2-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2111−1−3i32−1+3i32-2-2-2-21111−1−3i32−1+3i3211−1+3i32−1−3i32-2-21111−1−3i32−1+3i3211−1+3i32−1−3i32-2111−1−3i32−1+3i32-2111−1−3i32−1+3i320000000000000000000000000
χ48444-244-2-2-244-2111−1+3i32−1−3i32-2-2-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2111−1+3i32−1−3i32-2-2-2-21111−1+3i32−1−3i3211−1−3i32−1+3i32-2-21111−1+3i32−1−3i3211−1−3i32−1+3i32-2111−1+3i32−1−3i32-2111−1+3i32−1−3i320000000000000000000000000
χ49444-244-2-2-2-4-41-2−1−3i32−1+3i3211222211-2-2−1−3i32−1−3i32−1+3i32−1+3i3211111-2−1−3i32−1+3i3211-2-2-1-1221+3i321−3i32-1-11−3i321+3i32-1-1-1-1221+3i321−3i32-1-11−3i321+3i32-1-11-2−1−3i32−1+3i32111-2−1−3i32−1+3i32110000000000000000000000000
χ50444-244-2-2-2-4-41-2−1+3i32−1−3i3211222211-2-2−1+3i32−1+3i32−1−3i32−1−3i3211111-2−1+3i32−1−3i3211-2-2-1-1221−3i321+3i32-1-11+3i321−3i32-1-1-1-1221−3i321+3i32-1-11+3i321−3i32-1-11-2−1+3i32−1−3i32111-2−1+3i32−1−3i32110000000000000000000000000
χ51444-244-2-2-2-4-4-2111−1−3i32−1+3i322222-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2111−1−3i32−1+3i32-2-222-1-1-1-11+3i321−3i32-1-11−3i321+3i3222-1-1-1-11+3i321−3i32-1-11−3i321+3i32-2111−1−3i32−1+3i32-2111−1−3i32−1+3i320000000000000000000000000
χ52444-244-2-2-2-4-4-2111−1+3i32−1−3i322222-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2111−1+3i32−1−3i32-2-222-1-1-1-11−3i321+3i32-1-11+3i321−3i3222-1-1-1-11−3i321+3i32-1-11+3i321−3i32-2111−1+3i32−1−3i32-2111−1+3i32−1−3i320000000000000000000000000
χ53444-2-4-4-2-2-2001-2−1−3i32−1+3i3211−2i32i3−2i32i311-2-2−1−3i32−1−3i32−1+3i32−1+3i3211111-2−1−3i32−1+3i3211223-300−3−i323−i32i3i3−3+i323+i32−i3−i33-300−3−i323−i32i3i3−3+i323+i32−i3−i3-121+3i321−3i32-1-1-121+3i321−3i32-1-10000000000000000000000000
χ54444-2-4-4-2-2-2001-2−1−3i32−1+3i32112i3−2i32i3−2i311-2-2−1−3i32−1−3i32−1+3i32−1+3i3211111-2−1−3i32−1+3i321122-33003+i32−3+i32−i3−i33−i32−3−i32i3i3-33003+i32−3+i32−i3−i33−i32−3−i32i3i3-121+3i321−3i32-1-1-121+3i321−3i32-1-10000000000000000000000000
χ55444-2-4-4-2-2-2001-2−1+3i32−1−3i3211−2i32i3−2i32i311-2-2−1+3i32−1+3i32−1−3i32−1−3i3211111-2−1+3i32−1−3i321122-33003−i32−3−i32i3i33+i32−3+i32−i3−i3-33003−i32−3−i32i3i33+i32−3+i32−i3−i3-121−3i321+3i32-1-1-121−3i321+3i32-1-10000000000000000000000000
χ56444-2-4-4-2-2-2001-2−1+3i32−1−3i32112i3−2i32i3−2i311-2-2−1+3i32−1+3i32−1−3i32−1−3i3211111-2−1+3i32−1−3i3211223-300−3+i323+i32−i3−i3−3−i323−i32i3i33-300−3+i323+i32−i3−i3−3−i323−i32i3i3-121−3i321+3i32-1-1-121−3i321+3i32-1-10000000000000000000000000
χ57444-2-4-4-2-2-200-2111−1−3i32−1+3i32−2i32i3−2i32i3-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2111−1−3i32−1+3i3222003-3i3i3−3−i323−i32−i3−i3−3+i323+i32003-3i3i3−3−i323−i32−i3−i3−3+i323+i322-1-1-11+3i321−3i322-1-1-11+3i321−3i320000000000000000000000000
χ58444-2-4-4-2-2-200-2111−1−3i32−1+3i322i3−2i32i3−2i3-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2111−1−3i32−1+3i322200-33−i3−i33+i32−3+i32i3i33−i32−3−i3200-33−i3−i33+i32−3+i32i3i33−i32−3−i322-1-1-11+3i321−3i322-1-1-11+3i321−3i320000000000000000000000000
χ59444-2-4-4-2-2-200-2111−1+3i32−1−3i32−2i32i3−2i32i3-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2111−1+3i32−1−3i322200-33i3i33−i32−3−i32−i3−i33+i32−3+i3200-33i3i33−i32−3−i32−i3−i33+i32−3+i322-1-1-11−3i321+3i322-1-1-11−3i321+3i320000000000000000000000000
χ60444-2-4-4-2-2-200-2111−1+3i32−1−3i322i3−2i32i3−2i3-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2111−1+3i32−1−3i3222003-3−i3−i3−3+i323+i32i3i3−3−i323−i32003-3−i3−i3−3+i323+i32i3i3−3−i323−i322-1-1-11−3i321+3i322-1-1-11−3i321+3i320000000000000000000000000
χ6144-444-4-4-444-41-211-2-244-4-4-1-122-1-1-1-122221-211-2-24-411-2-211-2-211-2-2-1-122-1-122-1-1221-211-2-2-12-1-1220000000000000000000000000
χ6244-444-4-4-444-4-21-2-21144-4-422-1-12222-1-1-1-1-21-2-2114-4-2-211-2-211-2-21122-1-122-1-122-1-1-21-2-2112-122-1-10000000000000000000000000
χ6344-444-4-4-44-441-211-2-2-4-444-1-122-1-1-1-122221-211-2-24-4-1-122-1-122-1-12211-2-211-2-211-2-21-211-2-2-12-1-1220000000000000000000000000
χ6444-444-4-4-44-44-21-2-211-4-44422-1-12222-1-1-1-1-21-2-2114-422-1-122-1-122-1-1-2-211-2-211-2-211-21-2-2112-122-1-10000000000000000000000000
χ6544-44-44-4-44001-211-2-20000-1-122-1-1-1-122221-211-2-2-443-3003-3003-300-3300-3300-3300-12-1-1221-211-2-20000000000000000000000000
χ6644-44-44-4-44001-211-2-20000-1-122-1-1-1-122221-211-2-2-44-3300-3300-33003-3003-3003-300-12-1-1221-211-2-20000000000000000000000000
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Here i is the imaginary unit (i² = −1).