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×#32697 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2749 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
528 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)(12,13,18,22,17,23,35,43)(14,19,27,39,26,38,36,41)(15,28,31,32,30,20,40,25)(16,21,34,24,33,29,37,42);(12,14)(13,19)(15,29)(16,32)(17,26)(18,36)(20,37)(21,30)(22,41)(23,38)(24,31)(25,33)(27,35)(28,34)(39,43)(40,42);(12,15,17,30)(13,20)(14,24)(16,19,33,38)(18,31,35,40)(21,36)(22,25)(23,28)(26,42)(27,29)(32,43)(34,39,37,41);(12,16,17,33)(13,21,23,29)(14,25,26,32)(15,19,30,38)(18,37,35,34)(20,36,28,27)(22,42,43,24)(31,41,40,39)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 25685);