Finite Group DatabasebetaFinite Group Databasebeta| order | 30170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×D431 |
| Fitting, socle, Hall | C5×C7×C431 ⋊ C2 |
| derived, Sylow | C431 ⋊ C2×C5×C7 |
| Hall | C7×C431 ⋊ C2×C5 |
| Hall | C5×C431 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | D431 |
| commutator, cosocle, hypocenter | C431 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C431 | C2 |
| LCS | G ▷ C431 | |
| UCS | C1 ◁ C5×C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15085 |
7595 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30170, 3);