Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C4×#123×C47 ⋊ C2 |
| Sylow | C47 ⋊ #36604 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D47 |
| commutator, socle, cosocle | C23×C47 | C25 |
| Fitting | C4×#123×C47 | C2 |
| prime radical | #20248344 | C2 |
| hypercenter | C4×#123 | D47 |
| hypocenter | C47 | #36604 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C4×#123 | |
1888 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,47|a^2=h,b^2=h,c^2=fh,d^2=gh,e^2=fh,b^a=bf,c^a=cg,c^b=ch,e^b=eh,d^c=dh,i^c=i^46,e^d=eh,i^e=i^461358 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 375303);