Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12933 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12934 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1853 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
394 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)(14,15,18,25,20,26,19,24)(16,27,30,39,31,42,29,22)(17,32,34,41,36,40,35,23)(21,33,37,28,38,44,43,45);(14,16)(15,21,26,38)(17,33)(18,29)(19,30)(20,31)(22,23,39,41)(24,37,25,43)(27,40,42,32)(28,35)(34,45)(36,44);(14,16)(15,22)(17,28)(18,30)(19,29)(20,31)(21,23)(24,42)(25,27)(26,39)(32,37)(33,35)(34,44)(36,45)(38,41)(40,43)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5922);