Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1355 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#11911 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #329 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | #97 | C23×C11 |
| socle | C2×C11 | C2×#329 |
| prime radical | C11×#532 | C4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ C2×C11×#97 ◁ G | |
318 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(12,13,16,21,15,19,28,36,17,22,31,40,29,20,37,38)(14,23,25,41,26,18,32,33,27,34,42,39,24,35,30,43);(12,14)(13,18)(15,24)(16,30)(17,27)(19,23)(20,34)(21,39)(22,35)(25,37)(26,29)(28,42)(31,32)(33,36)(38,43)(40,41);(12,15,17,29)(13,19,22,20)(14,24,27,26)(16,28,31,37)(18,23,35,34)(21,36,40,38)(25,30,42,32)(33,41,43,39)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4899);