Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #453 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#21477 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C11 | #120 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | C4×#120 |
| prime radical | C11×#3018 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C11 ◁ C22×C8×C11 ◁ G | |
1290 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)(12,13,19,22,18,23,17,33)(14,24,27,20,28,37,34,38)(15,29,30,32,31,21,35,16)(25,39,41,36,42,26,40,43);(12,14)(13,20)(15,25)(16,26)(17,34)(18,28)(19,27)(21,36)(22,37)(23,38)(24,33)(29,43)(30,41)(31,42)(32,39)(35,40);(12,15)(13,21)(14,25)(16,22)(17,35)(18,31)(19,30)(20,36)(23,29)(24,39)(26,37)(27,41)(28,42)(32,33)(34,40)(38,43);(12,16,19,29,18,32,17,21)(13,15,22,30,23,31,33,35)(14,26,27,43,28,39,34,36)(20,25,37,41,38,42,24,40)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14465);