Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33758 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#33781 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C22×C11×D8 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
598 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
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)(15,17)(16,19)(20,21,25,30)(22,26,31,41)(23,27,36,44)(24,37,35,29)(28,45,43,34)(32,42,46,38)(33,50,47,40)(39,48,51,49);(12,14,15,19)(13,16,17,18)(20,22)(21,26)(23,32)(24,33)(25,31)(27,42)(28,39)(29,40)(30,41)(34,49)(35,47)(36,46)(37,50)(38,44)(43,51)(45,48);(14,19)(16,18)(21,27)(22,31)(23,34)(24,35)(26,38)(28,29)(30,44)(32,48)(36,45)(37,43)(39,50)(40,51)(41,42)(46,49);(13,17)(16,18)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26769);