Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C25×C42 |
No aliases for this group.
| Fitting | C11×#2811 ⋊ C2 |
| Sylow | C11 ⋊ #60048 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D11 |
| commutator, socle, cosocle | C23×C11 | C25 |
| Fitting | C11×#2811 | C2 |
| hypercenter | #2811 | D11 |
| hypocenter | C11 | #60048 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #2811 | |
2326 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1408 |
Polycyclic presentation:
2^8,11|a^2=fg,c^2=fgh,d^2=h,e^2=h,b^a=bf,c^a=cg,d^a=dg,e^a=ef,c^b=cg,d^b=dh,i^b=i^10,i^c=i^10,i^e=i^10224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1032938);