Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C43×#2586 ⋊ C2 |
| Sylow | C43 ⋊ #34840 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D43 |
| commutator, socle, cosocle | C23×C43 | C25 |
| Fitting | C43×#2586 | C2 |
| prime radical | C22×D172 | C23 |
| hypercenter | #2586 | D43 |
| hypocenter | C43 | #34840 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #2586 | |
1944 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,43|a^2=g,c^2=gh,e^2=f,b^a=bf,c^a=cg,i^a=i^42,c^b=ch,d^b=dh,i^b=i^42,i^d=i^42,i^e=i^42874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 339933);