Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C47×#529 ⋊ C2 |
| Sylow | C47 ⋊ #34829 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D47 |
| commutator, socle, cosocle | C23×C47 | C25 |
| Frattini | C23 | C24×D47 |
| Fitting | C2×C47×#529 | C2 |
| hypercenter | C2×#529 | D47 |
| hypocenter | C47 | #34829 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#529 | |
2804 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,47|c^2=gh,e^2=f,b^a=bf,c^a=cg,i^a=i^46,c^b=ch,d^b=dh,i^c=i^461364 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 339756);