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×#33776 |
| 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 | |
592 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)(22,31,34,49)(23,28,25,40)(24,36,39,50)(27,42,45,33)(29,35,47,38)(32,48,41,46)(37,43,51,44);(12,14,15,19)(13,16,17,18);(14,19)(16,18)(20,22)(21,27)(23,32)(24,37)(25,41)(26,34)(28,43)(29,46)(30,45)(31,36)(33,38)(35,42)(39,51)(40,44)(47,48)(49,50);(13,17)(16,18)(20,23,26,25)(21,28,30,40)(22,32,34,41)(24,35,39,38)(27,43,45,44)(29,36,47,50)(31,48,49,46)(33,37,42,51)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26764);