Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32894 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#32895 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2846 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
3540 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)(15,21)(16,25)(18,19)(23,38)(24,30)(26,40)(27,32)(28,31)(33,36)(34,39)(35,44)(41,42);(14,15)(16,22)(17,23)(18,30)(19,21)(20,24)(25,36)(26,35)(27,37)(28,34)(29,39)(31,38)(32,33)(40,45)(41,43)(42,44);(14,16,20,27)(15,22,24,37)(17,26,29,42)(18,25,19,32)(21,33,30,36)(23,35,39,44)(28,41,31,40)(34,43,38,45);(14,17)(15,23)(16,26)(18,31)(19,28)(20,29)(21,34)(22,35)(24,39)(25,40)(27,42)(30,38)(32,41)(33,43)(36,45)(37,44)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25883);