Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19186 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#19204 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C23×C11 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
646 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)(13,16)(14,18)(17,19)(20,21,25,29)(22,30,34,44)(23,27,35,41)(24,37,31,28)(26,38,40,33)(32,43,46,51)(36,48,45,42)(39,49,50,47);(20,22,31,38,25,34,24,33)(21,26,37,44,29,40,28,30)(23,32,45,49,35,46,36,47)(27,39,48,51,41,50,42,43);(12,13,15,17)(14,19,18,16)(20,23)(21,27)(22,32)(24,36)(25,35)(26,39)(28,42)(29,41)(30,43)(31,45)(33,47)(34,46)(37,48)(38,49)(40,50)(44,51);(23,35)(27,41)(32,46)(36,45)(39,50)(42,48)(43,51)(47,49)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12192);