Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#13455 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C23×C11 | AGL(1,ℤ/8) |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C11×#405 ◁ G | |
318 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)(12,13,16,18)(14,19,15,17)(20,21)(22,26)(23,27)(24,29)(25,31)(28,36)(30,37)(32,45)(33,42)(34,40)(35,41)(38,44)(39,46)(43,49)(47,51)(48,50);(12,14,16,15)(13,17,18,19)(20,22)(21,26)(23,33)(24,32)(25,35)(27,42)(28,39)(29,45)(30,40)(31,41)(34,37)(36,46)(38,47)(43,50)(44,51)(48,49);(12,15,16,14)(13,17,18,19)(21,27)(22,32)(23,36)(24,37)(26,39)(28,30)(29,43)(31,44)(33,47)(34,35)(38,49)(40,51)(41,50)(42,45)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6443);