Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#7450 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C11 | #357 |
| commutator | C2×C16 | C2×C4×C11 |
| Frattini, cosocle | C4×C16 | C22×C11 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C42×C11 ◁ C4×C8×C11 ◁ C4×C11×C16 ◁ G | |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2816 |
A minimal faithful permutation representation — 2 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16)(14,18)(17,19)(20,21,22,27,32,40,47,38,24,29,33,41,36,44,48,39,25,30,34,42,49,51,50,45,35,43,46,37,23,28,31,26);(12,13,15,17)(14,19,18,16)(21,26)(22,31)(23,32)(24,35)(27,28)(29,45)(30,39)(33,50)(34,48)(36,49)(37,40)(38,43)(41,51)(42,44)(46,47)539 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 438);