Finite Group DatabasebetaFinite Group Databasebeta| order | 32004 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C4×#22547878 |
| derived, Hall | C7×C127 ⋊ C4×C9 |
| Hall | C4×C7×C127 ⋊ C9 |
| Hall | C4×C127 ⋊ C7⋊C9 |
| Sylow | C127 ⋊ C4×C7⋊C9 |
| Hall | C4×C7 ⋊ #11765917 |
| Sylow | C7 ⋊ C4×#11765917 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | #14581888 |
| commutator, hypocenter | C7×C127 | C4×C9 |
| Frattini | C2×C3 | C2×#14581888 |
| Fitting | C3×C4×C7×C127 | C3 |
| socle, prime radical, cosocle | C2×C3×C7×C127 | C2×C3 |
| LCS | G ▷ C7×C127 | |
| UCS | C1 ◁ C3×C4 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32004 |
3588 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32004, 5);