Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23990 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#23992 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2404 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#585 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1128 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)(12,13,17,21)(14,18,24,32)(15,19,25,33)(16,27,29,20)(22,35,28,30)(23,37,38,31)(26,40,39,34)(36,42,41,43);(14,22,24,28)(18,30,32,35)(23,36,38,41)(31,42,37,43);(12,14)(13,18)(15,23)(16,28)(17,24)(19,31)(20,35)(21,32)(22,29)(25,38)(26,41)(27,30)(33,37)(34,43)(36,39)(40,42);(12,15)(13,19)(14,23)(16,26)(17,25)(18,31)(20,34)(21,33)(22,36)(24,38)(27,40)(28,41)(29,39)(30,42)(32,37)(35,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16980);