Finite Group DatabasebetaFinite Group Databasebeta| order | 12032 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C42 |
| direct product | D47×#2840 |
| Fitting | C47×#2840 ⋊ C2 |
| Sylow | C47 ⋊ C2×#2840 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D47 |
| commutator, socle, cosocle | C23×C47 | C25 |
| Fitting | C47×#2840 | C2 |
| prime radical | C25×D47 | C22 |
| hypercenter | #2840 | D47 |
| hypocenter | C47 | C2×#2840 |
| LCS | G ▷ C23×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
3550 conjugacy classes of subgroups; only the 579 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 579 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
650 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 375974);