Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2212 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#33594 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #459 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C2×C11 | C2×#459 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ C2×C4×C8×C11 ◁ G | |
696 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,23)(15,28)(16,22)(17,32)(18,33)(19,24)(20,26)(21,25)(27,40)(29,43)(30,39)(31,35)(34,36)(37,41)(38,42);(12,14,17,26,19,27,16,18)(13,20,22,23,24,33,32,40)(15,25,30,41,31,42,29,34)(21,35,36,39,38,28,37,43);(12,15)(13,21)(14,25)(16,29)(17,30)(18,34)(19,31)(20,35)(22,36)(23,39)(24,38)(26,41)(27,42)(28,33)(32,37)(40,43);(12,16,19,17)(13,22,24,32)(14,18,27,26)(15,29,31,30)(20,23,33,40)(21,36,38,37)(25,34,42,41)(28,43,35,39)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26582);