Finite Group DatabasebetaFinite Group Databasebeta| order | 32830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×D335 |
| unambiguous semidirect product | C5⋊(C72×D67) |
| unambiguous semidirect product | C67⋊(C72×D5) |
| Fitting, socle, Hall | C5×C72×C67 ⋊ C2 |
| derived, Hall | C5×C67 ⋊ C2×C72 |
| Hall | C72×C67 ⋊ D5 |
| Hall | C5×C72 ⋊ D67 |
| Sylow | C67 ⋊ C72×D5 |
| Sylow | C5 ⋊ C72×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D335 |
| commutator, cosocle, hypocenter | C5×C67 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C67 | C2 |
| LCS | G ▷ C5×C67 | |
| UCS | C1 ◁ C72 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16415 |
8281 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32830, 16);