Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | C11×#3444 ⋊ C2 |
| Sylow | C11 ⋊ #62694 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C23×D11 |
| commutator, socle, cosocle | C22×C11 | C26 |
| Frattini | C22 | C25×D11 |
| Fitting | C11×#3444 | C2 |
| hypercenter | #3444 | D11 |
| hypocenter | C11 | #62694 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C42 ◁ #3444 | |
6640 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^8,11|e^2=h,f^2=g,b^a=bg,c^a=ch,d^a=dg,c^b=cgh,d^b=dh,i^d=i^10356 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1076472);