Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42 |
No aliases for this group.
| Sylow | C47 ⋊ #13786 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D47 |
| commutator | C22×C47 | C22×C42 |
| Fitting | C47×C4⋊#95 | C2 |
| socle, prime radical, cosocle | C24×C47 | C24 |
| hypercenter | C4⋊#95 | D47 |
| hypocenter | C47 | #13786 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C24 ◁ C4⋊#95 | |
1862 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,47|a^2=g,b^2=h,c^2=efg,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,i^b=i^46,i^c=i^461376 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 90882);