Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1909 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#21009 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #386 |
| 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)(14,23)(15,28,30,20)(16,21)(17,31)(18,22)(19,26)(24,37,40,43)(25,34)(27,38)(29,36,32,35)(33,39,42,41);(12,14,17,26,18,27,16,25)(13,19,21,23,22,34,31,38)(15,24,32,41,30,40,29,39)(20,33,35,37,28,42,36,43);(12,15)(13,20)(14,24)(16,29)(17,32)(18,30)(19,33)(21,35)(22,28)(23,37)(25,39)(26,41)(27,40)(31,36)(34,42)(38,43);(12,16,18,17)(13,21,22,31)(14,25,27,26)(15,29,30,32)(19,23,34,38)(20,35,28,36)(24,39,40,41)(33,37,42,43)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 13997);