Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C4 |
No aliases for this group.
| Fitting | C2×C11×#389 ⋊ C2 |
| Sylow | C11 ⋊ #15140 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D11 |
| commutator, socle, cosocle | C24×C11 | C24 |
| Fitting | C2×C11×#389 | C2 |
| prime radical | C22×#66927 | C2 |
| hypercenter | C2×#389 | D11 |
| hypocenter | C11 | #15140 |
| LCS | G ▷ C24×C11 ▷ C11 | |
| UCS | C1 ◁ C24 ◁ C2×#389 | |
2854 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^8,11|a^2=ef,b^2=f,c^2=e,d^2=h,b^a=be,c^a=cf,d^a=dh,c^b=cg,i^b=i^10,i^c=i^10344 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 106263);