Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18992 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18998 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C2×C11×#562 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
926 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,18)(14,20,22,27)(15,23,25,19)(17,24,26,21)(28,29,32,35)(30,36,37,43)(31,39,40,34)(33,41,42,38);(12,14,16,22)(13,17,18,26)(15,24,25,21)(19,27,23,20)(31,40)(34,39)(36,43)(38,41);(15,25)(19,23)(20,27)(21,24)(28,30)(29,33)(31,41)(32,37)(34,43)(35,42)(36,39)(38,40);(13,18)(17,26)(19,23)(20,27)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11986);