Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#11978 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#102 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| prime radical | C11×#466 | C4 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
312 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,17)(14,15)(18,19)(20,21,23,29,37,43,50,45,24,27,38,28,25,30,39,47)(22,31,33,48,40,46,36,41,34,49,32,42,35,44,51,26);(12,13)(14,17)(15,19)(16,18)(20,22)(21,26)(23,36)(24,34)(25,40)(27,41)(28,44)(29,46)(30,48)(31,45)(32,39)(33,50)(35,37)(38,51)(42,43)(47,49);(12,14,16,15)(13,17,18,19)(21,27)(26,41)(28,29)(30,43)(31,49)(42,48)(44,46)(45,47)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4966);