Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23872 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#23873 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1686 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)(14,22)(15,26)(16,29)(17,21)(18,24)(19,27)(20,31)(23,34)(25,36)(28,37)(30,33)(32,35)(38,39)(40,42)(41,43);(12,14,17,25)(13,18,21,33)(15,23,28,40)(16,30,31,24)(19,34,35,42)(20,36,29,22)(26,38,37,43)(27,41,32,39);(16,31)(18,33)(20,29)(24,30)(26,37)(27,32)(34,42)(39,41);(12,15)(13,19)(14,23)(16,32)(17,28)(18,34)(20,37)(21,35)(22,38)(24,41)(25,40)(26,29)(27,31)(30,39)(33,42)(36,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16861);