Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#32696 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2749 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#535 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
552 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)(12,13,16,21,17,20,31,37)(14,22,25,38,24,18,30,33)(15,26,29,42,28,19,34,36)(23,39,27,41,40,32,43,35);(12,14)(13,18)(15,27)(16,30)(17,24)(19,35)(20,22)(21,38)(23,29)(25,31)(26,41)(28,43)(32,36)(33,37)(34,40)(39,42);(12,15)(13,19,20,26)(14,23,24,40)(16,29)(17,28)(18,32)(21,36,37,42)(22,39)(25,27,30,43)(31,34)(33,35)(38,41);(13,20)(16,31)(19,26)(25,30)(27,43)(29,34)(33,38)(35,41)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 25684);