Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33348 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33350 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C22×#99 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C2×D4 | C24×C11 |
| prime radical | C11×#3485 | C2 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×D4×C11 ◁ C2×C11×H(5,𝔽2) ◁ G | |
1240 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)(15,19)(16,28,29,20)(17,21)(18,24,31,38)(23,34)(25,35)(26,32)(27,40,39,33)(30,37,41,43)(36,42);(12,14,17,25)(13,18,21,31)(15,23,26,36)(16,24,29,38)(19,30,32,41)(20,22,28,35)(27,37,39,43)(33,34,40,42);(12,15)(13,19)(14,23)(16,27)(17,26)(18,30)(20,33)(21,32)(22,34)(24,37)(25,36)(28,40)(29,39)(31,41)(35,42)(38,43);(15,26)(19,32)(23,36)(27,39)(30,41)(33,40)(34,42)(37,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26338);