Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#18459 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
972 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,20)(16,24)(17,28)(21,34)(22,32)(23,29)(25,27)(26,41)(30,43)(33,38)(35,45)(36,42)(37,44)(39,40);(14,15,18,23)(16,21,25,35)(17,29,28,20)(19,22,31,37)(24,38,27,36)(26,42,40,33)(30,44,43,32)(34,39,45,41);(16,25)(17,30)(20,32)(21,35)(24,27)(26,39)(28,43)(29,44)(33,34)(36,38)(40,41)(42,45);(14,16,19,27)(15,21,22,36)(17,26,30,41)(18,25,31,24)(20,33,32,45)(23,35,37,38)(28,40,43,39)(29,42,44,34)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11447);