Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C42 |
No aliases for this group.
| Fitting | C2×C47×#392 ⋊ C2 |
| Sylow | C47 ⋊ #15142 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D47 |
| commutator, socle, cosocle | C24×C47 | C24 |
| Fitting | C2×C47×#392 | C2 |
| hypercenter | C2×#392 | D47 |
| hypocenter | C47 | #15142 |
| LCS | G ▷ C24×C47 ▷ C47 | |
| UCS | C1 ◁ C24 ◁ C2×#392 | |
4382 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,47|b^2=e,c^2=f,d^2=h,b^a=be,c^a=cf,d^a=dh,c^b=cg,i^d=i^461076 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 106272);