Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3003 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#17909 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C42 | C24×C11 |
| socle | C22×C11 | C2×C4×D4 |
| prime radical | C11×#449 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
626 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,21)(15,20)(16,24)(17,19)(18,22)(23,27)(25,26)(28,29,31,35,32,34,38,41)(30,33,36,40,37,39,42,43);(12,14)(13,18)(15,22)(16,25)(17,23)(19,26)(20,27)(21,24);(13,19)(18,26)(20,24)(21,27)(28,30,31,36,32,37,38,42)(29,33,35,40,34,39,41,43);(12,15,17,16)(13,20,19,24)(14,22,23,25)(18,27,26,21)(29,34)(33,39)(35,41)(40,43)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 10897);