Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #7307 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#7323 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #342 |
| commutator | C22×C4 | C42×C11 |
| Frattini, cosocle | C2×C4×Q8 | C22×C11 |
| prime radical | C23×C11 | #95 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C4×Q8×C11 ◁ G | |
256 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,17,15,16,18,19)(21,25,26,32)(27,35,34,33);(13,16)(14,18)(20,21,23,27,24,26,31,34)(22,25,28,33,29,32,30,35)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 311);