Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C42×Q8×C47 ⋊ C2 |
| Sylow | C47 ⋊ #36609 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D47 |
| commutator, socle, cosocle | C23×C47 | C25 |
| Fitting | C42×Q8×C47 | C2 |
| prime radical | C2×#13094021 | C22 |
| hypercenter | C42×Q8 | D47 |
| hypocenter | C47 | #36609 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C42×Q8 | |
1938 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,47|a^2=fh,b^2=fgh,c^2=fgh,d^2=gh,e^2=fh,b^a=bf,c^a=cg,i^a=i^46,c^b=ch,e^b=eh,d^c=dh,e^d=eh1910 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 375388);