Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33685 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#2186 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
546 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,21,23,28)(22,31,32,26)(24,27,35,42)(25,38,36,30)(29,44,43,37)(33,45,48,39)(34,41,49,47)(40,50,46,51);(13,16)(17,19)(20,22,23,32)(21,26,28,31)(24,33,35,48)(25,34,36,49)(27,39,42,45)(29,40,43,46)(30,41,38,47)(37,50,44,51);(21,27)(24,37)(25,36)(26,39)(28,42)(29,30)(31,45)(33,50)(34,49)(35,44)(38,43)(40,41)(46,47)(48,51);(12,14,15,18)(13,17,16,19)(22,32)(26,31)(33,48)(34,49)(39,45)(40,46)(41,47)(50,51)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26673);