Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7654 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#7671 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C24×C13 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C22×C42×C13 ◁ G | |
468 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20,21,18)(17,19)(23,27,28,29)(30,31,34,38,35,39,33,37)(32,40,43,36,41,45,42,44);(14,16,17,21)(15,18,19,20)(22,23)(24,27)(25,29)(26,28)(30,32)(31,36)(33,43)(34,42)(35,41)(37,45)(38,40)(39,44);(22,24,26,25)(23,27,28,29)(32,41)(36,44)(40,45)(42,43)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 659);