Finite Group DatabasebetaFinite Group Databasebeta| order | 30380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D49×D155 |
| unambiguous semidirect product | (C5×D49)⋊D31 |
| unambiguous semidirect product | (C31×D49)⋊D5 |
| Fitting, derived, Hall | C5×C31×C49 ⋊ C22 |
| Hall | C31×C49 ⋊ C2×D5 |
| Hall | C5×C49 ⋊ C2×D31 |
| Hall | C5×C31 ⋊ C2×D49 |
| Sylow | C49 ⋊ C2×D155 |
| Sylow | C31 ⋊ D5×D49 |
| Sylow | C5 ⋊ D31×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C31×C49 | C22 |
| Frattini | C7 | D7×D155 |
| socle | C5×C7×C31 | C2×D7 |
| LCS | G ▷ C5×C31×C49 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7595 |
2054 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30380, 27);