Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#33777 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#2184 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
608 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)(22,31)(23,28)(24,27)(25,38)(26,32)(29,37)(30,36)(33,39)(34,41)(35,43)(40,49)(42,47)(44,51)(45,50)(46,48);(12,14,15,19)(13,16,17,18)(20,22)(21,26)(23,32)(24,33)(25,34)(27,42)(28,31)(29,40)(30,41)(35,47)(36,48)(37,50)(38,46)(39,43)(44,45)(49,51);(14,19)(16,18)(21,27)(22,32)(24,37)(25,36)(26,39)(28,43)(29,30)(31,42)(33,49)(35,51)(38,44)(40,46)(41,45)(47,50);(13,17)(16,18)(21,28)(26,31)(27,43)(29,44)(30,38)(39,42)(40,45)(41,46)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26765);