Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18419 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3537 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1062 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)(12,13,17,22)(14,24,27,40)(15,21,16,31)(18,23,34,39)(19,32,37,25)(20,33,29,30)(26,35,28,42)(36,41,38,43);(12,14)(13,19)(15,25)(16,32)(17,27)(18,28)(20,35)(21,40)(22,37)(23,38)(24,31)(26,34)(29,42)(30,41)(33,43)(36,39);(12,13)(14,19)(15,29)(16,20)(17,22)(18,23)(21,33)(24,41)(25,42)(26,36)(27,37)(28,38)(30,31)(32,35)(34,39)(40,43);(12,15,17,16)(13,20,22,29)(14,25,27,32)(18,30,34,33)(19,35,37,42)(21,39,31,23)(24,38,40,36)(26,43,28,41)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11407);