Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7447 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#7448 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #1361 |
| commutator | C2×C16 | C2×C4×C11 |
| Frattini, cosocle | C4×C16 | C22×C11 |
| prime radical | C11×#2246 | C2 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C4×C8×C11 ◁ C4×C11×C16 ◁ G | |
146 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 146 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)(12,13,15,21,31,24,33,40,18,25,32,23,17,34,16,22)(14,26,28,20,39,38,43,37,30,41,42,36,29,19,27,35);(13,19)(14,27)(15,16)(17,31)(20,23)(21,36)(22,35)(24,41)(25,38)(26,34)(28,29)(30,43)(32,33)(37,40)(39,42)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 436);