Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33756 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G | |
594 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)(22,27)(23,33)(24,36)(25,40)(26,30)(28,34)(29,38)(31,47)(32,46)(35,50)(37,42)(39,49)(41,45)(43,51)(44,48);(12,14)(13,16)(15,19)(17,18)(20,22,26,25)(21,27,30,40)(23,31,35,41)(24,32,39,38)(28,42,44,43)(29,36,46,49)(33,47,50,45)(34,37,48,51);(14,19)(16,18)(20,23,26,35)(21,28,30,44)(22,31,25,41)(24,37,39,51)(27,42,40,43)(29,45,46,47)(32,48,38,34)(33,49,50,36);(13,17)(16,18)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26744);