Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1412 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#7503 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #354 |
| 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 | |
270 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 270 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) = 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)(12,13,15,20)(14,23,25,40)(16,21,30,38)(17,22,28,39)(18,32,33,42)(19,29,36,31)(24,35,41,37)(26,34,27,43);(12,14)(13,18)(15,27,28,32)(16,26)(17,24)(19,35)(20,37,39,40)(21,23)(22,34)(25,30,41,29)(31,42)(33,36,43,38)308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 491);