Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11867 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#11867 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1519 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C2×M16 | C23×C13 |
| prime radical | C13×#3060 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C2×C4×C13 ◁ C2×C13×#131 ◁ G | |
376 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)(16,26)(17,30,34,20)(18,23)(19,25)(21,27)(22,31,36,44)(24,33)(28,38,32,37)(29,39)(35,45,41,42)(40,43);(15,20)(16,27)(17,31)(18,33)(21,37)(22,24)(23,36)(25,30)(26,41)(28,32)(29,43)(34,44)(35,39)(38,40);(14,16,18,27,19,29,33,43)(15,21,24,26,25,40,23,39)(17,32,31,45,34,28,44,42)(20,35,36,38,30,41,22,37)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 4855);