Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C32 · Schur multiplier (H2) = C8 |
| direct product | C8×C47⋊C32 |
| derived, Sylow | C47 ⋊ C8×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8×C16 | D47 |
| commutator, hypocenter | C47 | C8×C32 |
| Frattini | C4×C16 | C2×D47 |
| Fitting | C8×C16×C47 | C2 |
| socle, prime radical | C22×C47 | C4×C16 |
| cosocle | C4×C16×C47 | C22 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C8×C16 | |
134 conjugacy classes of subgroups.
3200 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 56894);