Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#7497 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #353 |
| commutator | C42 | C42×C11 |
| Frattini, cosocle | #532 | C22×C11 |
| socle | C2×C11 | #1393 |
| prime radical | C11×#532 | C22 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C2×C4×C11 ◁ C22×C4×C11 ◁ C11×#532 ◁ G | |
290 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 176 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,19)(15,17,21,25)(16,20,22,27)(18,23,26,24);(13,17,20,18)(14,21,22,23)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 485);