Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#22898 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | D42 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | #2358 |
| prime radical | C11×#3018 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ G | |
996 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,22,17,23,32,21)(14,20,26,35,27,34,25,18)(15,28,29,38,31,37,30,19)(24,39,41,43,42,33,40,36);(12,14,16,26,17,27,32,25)(13,18,22,20,23,35,21,34)(15,24,29,41,31,42,30,40)(19,33,28,36,38,39,37,43);(12,15)(13,19)(14,24)(16,29)(17,31)(18,33)(20,36)(21,37)(22,28)(23,38)(25,40)(26,41)(27,42)(30,32)(34,43)(35,39);(12,14)(13,20)(15,24)(16,26)(17,27)(18,21)(19,36)(22,35)(23,34)(25,32)(28,39)(29,41)(30,40)(31,42)(33,37)(38,43)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15886);