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×#18464 |
| 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 | |
970 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)(17,29)(21,34)(22,32)(23,30)(25,28)(27,42)(31,41)(33,38)(35,45)(36,44)(37,43)(39,40);(14,15,18,23)(16,21,25,35)(17,30,29,20)(19,22,26,36)(24,38,28,37)(27,43,40,33)(31,44,41,32)(34,39,45,42);(16,25)(17,31)(20,32)(21,35)(24,28)(27,39)(29,41)(30,44)(33,34)(37,38)(40,42)(43,45);(14,16,26,24)(15,21,36,38)(17,27,41,39)(18,25,19,28)(20,33,44,34)(22,37,23,35)(29,40,31,42)(30,43,32,45)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 11452);