Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | Q8×#41×C43 ⋊ C2 |
| Sylow | C43 ⋊ #62752 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C24×D43 |
| commutator, socle, cosocle | C22×C43 | C26 |
| Frattini | C22 | C25×D43 |
| Fitting | Q8×#41×C43 | C2 |
| hypercenter | Q8×#41 | D43 |
| hypocenter | C43 | #62752 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ Q8×#41 | |
6528 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,43|b^2=h,d^2=h,f^2=g,b^a=bg,c^a=ch,d^a=dg,e^a=eh,i^a=i^42,c^b=cg,d^b=dh,i^c=i^42,i^d=i^42,i^e=i^421126 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 1077313);