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×#33782 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
588 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)(15,17)(16,19)(20,21,26,30)(22,31,32,48)(23,28,25,40)(24,36,39,50)(27,42,43,34)(29,35,47,38)(33,49,41,46)(37,44,51,45);(12,14,15,19)(13,16,17,18)(22,32)(27,43)(31,48)(33,41)(34,42)(37,51)(44,45)(46,49);(14,19)(16,18)(20,22)(21,27)(23,33)(24,37)(25,41)(26,32)(28,44)(29,46)(30,43)(31,36)(34,38)(35,42)(39,51)(40,45)(47,49)(48,50);(13,17)(16,18)(20,23,26,25)(21,28,30,40)(22,33,32,41)(24,35,39,38)(27,44,43,45)(29,36,47,50)(31,49,48,46)(34,37,42,51)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26770);