Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11×C16 · Schur multiplier (H2) = C22×C4 |
| direct product | C11×#11493 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C11 | C22⋊C4 |
| commutator | C22 | C22×C11×C16 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C22×C11 | C2×C22⋊C8 |
| prime radical | C23×C11 | C22×C8 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C11 ◁ C2×C4×C8×C11 ◁ G | |
342 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,20,22,17)(15,18)(16,19)(21,26,27,24)(23,25)(28,29,31,35,32,36,40,43,33,37,30,34,38,41,39,42);(12,14,16,22)(13,17,19,20)(15,21,23,27)(18,24,25,26);(12,15,16,23)(13,18,19,25)(14,21,22,27)(17,24,20,26)(28,30,32,39,33,31,38,40)(29,34,36,42,37,35,41,43)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4481);