Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33677 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#466 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
548 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)(22,30)(23,26)(24,36)(25,39)(27,32)(28,38)(29,35)(31,46)(33,50)(34,47)(37,45)(40,44)(41,48)(42,49)(43,51);(13,16)(17,19)(21,26)(27,41)(28,42)(29,39)(30,46)(36,47)(43,45)(44,50);(20,22,23,31)(21,27,26,41)(24,37,34,51)(25,40,35,33)(28,44,42,50)(29,45,39,43)(30,47,46,36)(32,49,48,38);(12,14,15,18)(13,17,16,19)(22,31)(27,41)(30,46)(32,48)(33,40)(37,51)(43,45)(44,50)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26665);