Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24×C42 |
| direct product | C13×#17309 |
| 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 | |
1466 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)(19,21)(22,23,25,27)(24,28,29,26)(30,31)(32,35)(33,34)(36,37)(40,44)(42,45);(16,20)(19,21)(24,29)(26,28)(31,34)(35,36)(38,39,41,43)(40,45,44,42);(14,15)(16,19)(17,18)(20,21)(22,23)(24,26)(25,27)(28,29)(30,32)(31,35)(33,37)(34,36)(38,40,41,44)(39,42,43,45);(14,16)(15,19)(17,20)(18,21)(22,24,25,29)(23,26,27,28)(30,31)(32,36)(33,34)(35,37)(38,39)(40,42)(41,43)(44,45)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10297);