Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C4 |
No aliases for this group.
| Sylow | C47 ⋊ #15140 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D47 |
| commutator, socle, cosocle | C24×C47 | C24 |
| Fitting, prime radical | C22×#127×C47 | C2 |
| hypercenter | C22×#127 | D47 |
| hypocenter | C47 | #15140 |
| LCS | G ▷ C24×C47 ▷ C47 | |
| UCS | C1 ◁ C24 ◁ C22×#127 | |
2854 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,47|a^2=ef,b^2=f,c^2=e,d^2=h,b^a=be,c^a=cf,d^a=dh,i^a=i^46,c^b=cg,i^b=i^46,i^c=i^461352 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 106266);