Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33638 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33638 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×#476 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
514 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)(16,26,28,44)(17,19)(18,30)(22,36,37,40)(23,25)(27,31,33,43)(29,32)(34,38,42,45)(35,41);(14,15,17,21,20,23,19,25)(16,22,27,34,28,37,33,42)(18,24,29,35,32,39,30,41)(26,38,43,36,44,45,31,40);(14,16)(15,22)(17,27)(18,31)(19,33)(20,28)(21,34)(23,37)(24,40)(25,42)(26,29)(30,44)(32,43)(35,38)(36,39)(41,45);(15,23)(21,25)(22,37)(24,39)(34,42)(35,41)(36,40)(38,45)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26626);