Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9263 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#9264 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #386 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C11×#3188 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
504 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,18,21,27)(14,23,25,35)(15,19)(22,33,32,34)(24,42,28,26)(30,36)(31,41)(37,38);(12,13,19,34,29,32,30,18)(14,20,35,38,42,43,24,31)(15,27,17,21,36,33,16,22)(23,41,26,39,28,37,25,40);(12,14)(13,20)(15,28)(16,26)(17,25)(18,31)(19,35)(21,40)(22,39)(23,36)(24,30)(27,37)(29,42)(32,43)(33,41)(34,38)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2252);