Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33359 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33361 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C22×#99 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C2×D4 | C24×C11 |
| prime radical | C11×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×D4×C11 ◁ C2×C11×H(5,𝔽2) ◁ G | |
1252 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)(14,22,25,35)(15,19)(16,28,30,20)(17,21)(18,24)(23,36,37,43)(26,33)(27,40,39,34)(29,32)(31,38)(41,42);(12,14,17,25)(13,18,21,32)(15,23,26,37)(16,29,30,24)(19,31,33,42)(20,35,28,22)(27,41,39,38)(34,43,40,36);(12,15)(13,19)(14,23)(16,27)(17,26)(18,31)(20,34)(21,33)(22,36)(24,38)(25,37)(28,40)(29,41)(30,39)(32,42)(35,43);(15,26)(19,33)(23,37)(27,39)(31,42)(34,40)(36,43)(38,41)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26349);