Finite Group DatabasebetaFinite Group Databasebeta| order | 32830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C67 · Schur multiplier (H2) = C7 |
| direct product | C67×C5⋊(C7⋊D7) |
| unambiguous semidirect product | C5⋊(C67×C7⋊D7) |
| unambiguous semidirect product | C7⋊(C67×D35) |
| Fitting, socle, Hall | C5×C72×C67 ⋊ C2 |
| derived, Hall | C5×C72 ⋊ C2×C67 |
| Hall | C72×C67 ⋊ D5 |
| Hall | C5×C67 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ D5×C67 |
| Sylow | C5 ⋊ C67×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | C5⋊(C7⋊D7) |
| commutator, cosocle, hypocenter | C5×C72 | C2×C67 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C67 | C2 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C67 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16415 |
8308 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32830, 19);