Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23892 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#23892 |
| 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 | |
1674 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)(14,24)(15,30)(16,34)(17,22)(18,23)(19,27)(20,32)(21,31)(25,41)(26,36)(28,38)(29,37)(33,40)(35,42)(39,43);(12,14)(13,19)(15,26)(16,28)(17,27)(18,29)(20,39)(21,36)(22,37)(23,38)(24,34)(25,31)(30,35)(32,42)(33,43)(40,41);(12,15)(13,20)(14,25)(16,31)(17,32)(18,33)(19,35)(21,23)(22,40)(24,36)(26,27)(28,43)(29,42)(30,34)(37,39)(38,41);(12,15)(13,21)(14,26)(16,32)(17,31)(18,33)(19,36)(20,23)(22,40)(24,35)(25,27)(28,42)(29,43)(30,34)(37,41)(38,39)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16880);