Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C22×C11×#121 ⋊ C2 |
| Sylow | C11 ⋊ #36717 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D11 |
| commutator, socle, cosocle | C23×C11 | C25 |
| Fitting | C22×C11×#121 | C2 |
| hypercenter | C22×#121 | D11 |
| hypocenter | C11 | #36717 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C22×#121 | |
3394 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^8,11|a^2=g,d^2=f,b^a=bf,c^a=cg,d^a=df,e^a=efh,i^a=i^10,c^b=ch,d^b=dfh332 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 376536);