Finite Group DatabasebetaFinite Group Databasebeta| order | 30380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| Fitting, derived, Hall | C31×C49 ⋊ C22×C5 |
| Hall | C49×ΓL(1,𝔽32) ⋊ C22 |
| Hall | D31×D49 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C2×D49 |
| Sylow | C49 ⋊ C2×D31⋊C5 |
| Sylow | C31 ⋊ C2×C5×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C31×C49 | C22×C5 |
| Frattini | C7 | D7×D31⋊C5 |
| socle | C7×C31 | C2×C5×D7 |
| LCS | G ▷ C31×C49 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1519 |
338 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30380, 14);