Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11858 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#11979 |
| 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 | |
306 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)(20,21,24,30,25,31,39,45,26,28,40,46,38,47,23,29)(22,32,34,42,35,48,33,49,36,50,37,27,41,43,51,44);(12,13)(14,17)(15,19)(16,18)(20,22)(21,27)(23,37)(24,33)(25,41)(26,36)(28,42)(29,48)(30,32)(31,49)(34,39)(35,38)(40,51)(43,45)(44,47)(46,50);(12,14,16,15)(13,17,18,19)(21,28)(27,42)(29,45)(30,46)(31,47)(32,50)(43,48)(44,49)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4967);