Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#24672 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
754 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)(14,18)(15,16)(17,19)(20,21,24,29,26,31,25,30)(22,27,33,42,34,43,40,47)(23,35,37,46,39,45,38,28)(32,44,36,50,48,51,49,41);(13,16)(17,18)(20,22)(21,27)(23,36)(24,33)(25,40)(26,34)(28,44)(29,42)(30,47)(31,43)(32,38)(35,50)(37,48)(39,49)(41,45)(46,51);(20,23,26,39)(21,28,31,46)(22,32,34,48)(24,38,25,37)(27,41,43,50)(29,45,30,35)(33,49,40,36)(42,51,47,44);(12,14,15,19)(13,17,16,18)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17660);