Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10690 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#10691 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #401 |
| commutator, Frattini, cosocle | C25 | C23×C11 |
| prime radical | C25×C11 | C23 |
| LCS | G ▷ C25 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C25×C11 ◁ G | |
372 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,23,26,35)(15,27,30,36)(16,20)(17,22)(18,25,34,41)(19,29,37,31)(21,32)(24,38,28,43)(33,40,42,39);(12,14)(13,18,22,35)(15,28,29,39)(16,26)(17,25)(19,33,37,38)(20,34,21,23)(24,30,40,31)(27,42,36,43)(32,41);(12,15)(13,19,20,36)(14,24,25,28)(16,29)(17,31)(18,33,23,38)(21,37,22,27)(26,40,41,39)(30,32)(34,43,35,42)275 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3679);