Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | C43×#3566 ⋊ C2 |
| Sylow | C43 ⋊ #62827 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D43 |
| commutator, socle, cosocle | C22×C43 | C26 |
| Fitting | C43×#3566 | C2 |
| hypercenter | #3566 | D43 |
| hypocenter | C43 | #62827 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #3566 | |
At least 6428 conjugacy classes of subgroups; only the 3213 normal subgroups are shown.
Polycyclic presentation:
2^8,43|c^2=h,d^2=g,e^2=g,b^a=bg,c^a=ch,d^a=dg,f^a=fh,c^b=cg,e^b=eh,i^c=i^42,i^d=i^42,i^e=i^42,i^f=i^42874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 1078320);