Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C47×#388 ⋊ C2 |
| Sylow | C47 ⋊ #36795 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D47 |
| commutator, socle, cosocle | C23×C47 | C25 |
| Fitting | C2×C47×#388 | C2 |
| hypercenter | C2×#388 | D47 |
| hypocenter | C47 | #36795 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C2×#388 | |
1950 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,47|b^2=g,c^2=f,d^2=g,b^a=bf,c^a=cg,d^a=df,e^a=efh,i^a=i^46,c^b=ch,d^b=dfh1340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 378492);