Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33691 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33691 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #3109 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#2190 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C11×#405 ◁ G | |
524 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)(14,22)(15,26)(16,30)(18,31)(20,35)(21,34)(23,28)(24,39)(25,40)(27,41)(29,42)(32,43)(33,38)(36,37);(12,13)(14,18)(15,27)(16,21)(17,19)(20,29)(22,38)(23,37)(24,33)(25,32)(26,41)(28,43)(30,34)(31,39)(35,42)(36,40);(12,14)(13,18)(15,28)(16,23)(17,24)(19,33)(20,36)(21,37)(22,26)(25,30)(27,43)(29,40)(31,35)(32,34)(38,41)(39,42);(13,19)(14,23,24,25)(15,29)(18,32,33,37)(21,34)(22,28,39,40)(26,42)(31,43,38,36)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26679);