Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13396 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13396 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#3058 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
422 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(16,25)(17,30)(18,19)(21,35)(22,37)(23,34)(26,38)(27,42)(28,43)(29,31)(32,33)(36,45)(39,44)(40,41);(14,15)(16,26)(17,22)(18,34)(19,23)(20,24)(21,28)(25,41)(27,40)(29,36)(30,37)(31,35)(32,44)(33,39)(38,42)(43,45);(14,16,19,28,20,27,18,29)(15,21,23,40,24,36,34,26)(17,31,30,42,33,43,32,25)(22,38,37,45,39,41,44,35)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6384);