Finite Group DatabasebetaFinite Group Databasebeta| order | 30380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| direct product | D31×C5⋊(C7⋊D7) |
| unambiguous semidirect product | (C5×D31)⋊(C7⋊D7) |
| unambiguous semidirect product | (C7×D31)⋊D35 |
| Fitting, socle, derived, Hall | C5×C72×C31 ⋊ C22 |
| Hall | C72×C31 ⋊ C2×D5 |
| Hall | C5×C72 ⋊ C2×D31 |
| Hall | C5×C31 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ D5×D31 |
| Sylow | C31 ⋊ C2×C5⋊(C7⋊D7) |
| Sylow | C5 ⋊ D31×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72×C31 | C22 |
| LCS | G ▷ C5×C72×C31 | |
| UCS | C1 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7595 |
2108 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30380, 99);