Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C11×#1619 ⋊ C2 |
| Sylow | C11 ⋊ D82 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #10623121 |
| commutator, cosocle | C42×C11 | C24 |
| Frattini | C42 | C23×D11 |
| Fitting | C11×#1619 | C2 |
| socle | C22×C11 | D42 |
| hypercenter | #1619 | D11 |
| hypocenter | C11 | D82 |
| LCS | G ▷ C42×C11 ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #1619 | |
918 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^8,11|e^2=g,f^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eg,f^a=fh,d^b=de,e^b=eg,f^c=fh,e^d=eg,i^d=i^10179 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 161912);