Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C11 ⋊ #34861 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D11 |
| commutator, socle, cosocle | C23×C11 | C25 |
| Frattini | C23 | C24×D11 |
| Fitting, prime radical | C11×#2388 | C2 |
| hypercenter | #2388 | D11 |
| hypocenter | C11 | #34861 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C22×C4 ◁ #2388 | |
2062 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^8,11|c^2=h,d^2=g,e^2=f,b^a=bf,c^a=cg,c^b=ch,d^b=dh,i^d=i^10296 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 340243);