Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of B(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#10937 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #120 |
| commutator | C23 | C2×C42×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #386 |
| prime radical | C25×C11 | C2×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
1066 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17,20,24,21,19,23,28)(18,25,27,31,26,22,29,30);(12,13,14,15)(16,18)(17,22)(19,25)(20,29)(21,26)(23,27)(24,31)(28,30);(16,19,20,28,21,17,23,24)(18,25,29,30,26,22,27,31)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 3925);