Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1406 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C11 · Schur multiplier (H2) = C2×C4 |
| direct product | C11×#7352 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #353 |
| commutator | C42 | C2×C8×C11 |
| Frattini, cosocle | #382 | C22×C11 |
| prime radical | C2×C11×#127 | C4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C11 ◁ C22×C4×C11 ◁ C11×#382 ◁ G | |
256 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 256 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) = 35 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,16,15,17,18,19)(20,21,22,27)(23,26,29,34)(24,28,30,35)(25,31,33,32);(21,25)(22,29)(23,32)(26,28)(30,31)(33,34)308 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 340);