Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7389 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#7389 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #1333 |
| commutator | C16 | C2×C8×C11 |
| Frattini, cosocle | #346 | C22×C11 |
| prime radical | C11×#508 | C4 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C4×C8×C11 ◁ C11×#346 ◁ G | |
118 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 50 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 — 2 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,18,19,33,21,35,22,36)(14,23,26,39)(15,28)(16,30)(20,24,29,40,32,41,38,34)(25,37)(27,43,42,31);(12,13)(14,24)(15,29)(16,19)(17,21)(18,31)(20,37)(22,30)(23,33)(25,38)(26,41)(27,34)(28,32)(35,43)(36,39)(40,42)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 377);