Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #13609 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#13609 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2127 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | #127 | C23×C11 |
| prime radical | C11×#3220 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C11 ◁ C22×C4×C11 ◁ C11×#535 ◁ G | |
348 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 86 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)(14,23,25,18)(15,19)(16,21,31,20)(17,22)(24,38,39,32)(26,33,30,34)(27,40,41,43)(28,36)(29,35,42,37);(12,14)(13,18)(15,27)(16,30)(17,26)(19,32)(20,33)(21,23)(22,34)(24,28)(25,31)(29,39)(35,38)(36,43)(37,40)(41,42);(12,15)(13,19)(14,24)(16,29)(17,28)(18,32)(20,37)(21,35)(22,36)(23,38)(25,39)(26,27)(30,41)(31,42)(33,40)(34,43)275 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6597);