Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3019 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#20947 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C2×#120 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | C2×#386 |
| prime radical | C11×#3449 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
1708 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)(14,22,25,36)(15,26,28,19)(16,21)(17,20)(18,24,33,29)(23,38)(27,37,30,34)(31,35)(32,39)(40,43)(41,42);(12,14,16,29,17,25,31,24)(13,18,21,36,20,33,35,22)(15,23,30,39,28,40,27,41)(19,32,37,43,26,42,34,38);(12,15)(13,19)(14,23)(16,30)(17,28)(18,32)(20,26)(21,37)(22,38)(24,41)(25,40)(27,31)(29,39)(33,42)(34,35)(36,43);(13,20)(18,33)(19,26)(21,35)(22,36)(32,42)(34,37)(38,43)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 13935);