Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C11×#395 ⋊ C2 |
| Sylow | C11 ⋊ #14723 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D11 |
| commutator, socle, cosocle | C24×C11 | C24 |
| Fitting | C2×C11×#395 | C2 |
| prime radical | C23×D44 | C22 |
| hypercenter | C2×#395 | D11 |
| hypocenter | C11 | #14723 |
| LCS | G ▷ C24×C11 ▷ C11 | |
| UCS | C1 ◁ C24 ◁ C2×#395 | |
2558 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^8,11|a^2=e,b^2=e,d^2=e,b^a=be,c^a=cf,d^a=dh,c^b=cg,i^c=i^10,i^d=i^10284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 101019);