Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9946 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#9958 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C11 |
| prime radical | C2×C11×#121 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
594 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,21)(14,22,24,26)(15,18,16,20)(19,25,27,23)(28,29)(30,33)(31,34)(32,35)(36,39)(37,40)(38,42)(41,43);(13,18)(15,16)(19,22)(20,21)(23,25)(26,27)(28,30,32,37)(29,33,35,40)(31,36,38,43)(34,41,42,39);(12,14)(13,19)(15,23)(16,25)(17,24)(18,26)(20,22)(21,27)(28,31)(29,34)(30,36)(32,38)(33,39)(35,42)(37,43)(40,41)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 2946);