Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C13×#17298 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C13 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C13 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ G | |
970 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,18)(16,20)(22,23)(24,27)(25,26)(28,29)(30,31,33,35)(32,34,36,37)(39,42)(40,44);(16,20)(19,21)(23,25)(24,28)(32,36)(34,37)(38,39,41,42)(40,43,44,45);(14,15,17,18)(16,19,20,21)(22,24,26,28)(23,27,25,29)(30,32)(31,34)(33,36)(35,37)(38,39)(40,45)(41,42)(43,44);(14,16,17,20)(15,19,18,21)(22,25,26,23)(24,27,28,29)(30,31)(32,34)(33,35)(36,37)(38,40)(39,43)(41,44)(42,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10286);