Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C43×#2698 ⋊ C2 |
| Sylow | C43 ⋊ #36716 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D43 |
| commutator, socle, cosocle | C23×C43 | C25 |
| Fitting | C43×#2698 | C2 |
| prime radical | C2×#14583488 | C2 |
| hypercenter | #2698 | D43 |
| hypocenter | C43 | #36716 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #2698 | |
2406 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,43|a^2=g,b^2=f,c^2=f,b^a=bf,c^a=cg,d^a=df,e^a=efh,c^b=ch,d^b=dfh,i^d=i^42,i^e=i^42724 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 376514);