Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12948 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12949 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1864 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ 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)(14,15,19,26,21,27,20,38)(16,28,30,42,32,39,31,43)(17,33,36,25,18,22,34,24)(23,35,40,29,41,37,44,45);(15,22,27,33)(17,34)(18,36)(19,20)(23,39,41,28)(24,26,25,38)(29,35)(30,31)(37,45)(40,42,44,43);(14,16)(15,23)(17,35)(18,37)(19,31)(20,30)(21,32)(22,39)(24,42)(25,43)(26,44)(27,41)(28,33)(29,34)(36,45)(38,40)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5937);