Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17597 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#17598 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3520 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C4×D4×C13 ◁ G | |
996 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)(15,20,22,34)(16,25)(17,28)(21,36,38,44)(23,35,24,29)(26,40)(27,43)(30,32)(33,37,45,39)(41,42);(14,15,18,23)(16,21,26,37)(17,29,28,34)(19,24,31,22)(20,32,35,30)(25,39,40,38)(27,36,42,45)(33,43,44,41);(14,16)(15,21)(17,27)(18,26)(19,25)(20,33)(22,38)(23,37)(24,39)(28,42)(29,36)(30,41)(31,40)(32,43)(34,45)(35,44);(16,26)(21,37)(25,40)(27,42)(33,44)(36,45)(38,39)(41,43)637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10586);