Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1284 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#7146 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #95 |
| commutator | C2×C4 | C4×C8×C11 |
| Frattini, cosocle | C2×C4×C8 | C22×C11 |
| socle | C22×C11 | #336 |
| prime radical | C23×C11 | C4⋊C8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
210 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 1408 |
A minimal faithful permutation representation — 2 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,21,23,27)(15,19)(16,25)(17,20)(18,22,26,24)(28,29,31,36,32,35,39,42,33,37,40,43,30,34,38,41);(12,14,16,24,17,23,15,22)(13,18,19,21,20,26,25,27)(29,34,37,35)(36,41,43,42)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 134);