Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#11591 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C11 | D8 |
| commutator | C8 | C22×C8×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle | C22×C11 | C2×#102 |
| prime radical | C2×C11×#135 | C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
402 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,16,15,17,18,19)(20,21)(22,31)(23,28)(24,36)(25,40)(26,30)(27,33)(29,38)(32,47)(34,48)(35,46)(37,42)(39,50)(41,45)(43,51)(44,49);(20,22)(21,27)(23,32)(24,37)(25,41)(26,34)(28,42)(29,45)(30,44)(31,36)(33,38)(35,49)(39,51)(40,43)(46,47)(48,50);(20,23,26,25)(21,28,30,40)(22,32,34,41)(24,35,39,38)(27,42,44,43)(29,36,46,50)(31,47,48,45)(33,37,49,51)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4579);