Finite Group DatabasebetaFinite Group Databasebeta| order | 30380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×D49×ΓL(1,𝔽32) |
| unambiguous semidirect product | C49⋊(C22×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C2×C49)⋊(C2×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C2×C31×D49)⋊C5 |
| Fitting | C2×C31×C49 ⋊ C2×C5 |
| derived, Hall | C31×C49 ⋊ C22×C5 |
| Hall | C49×ΓL(1,𝔽32) ⋊ C22 |
| Hall | C2×C31×D49 ⋊ C5 |
| Sylow | C49 ⋊ C22×ΓL(1,𝔽32) |
| Sylow | C31 ⋊ C2×C5×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D49×ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31×C49 | C22×C5 |
| Frattini | C7 | C2×D7×ΓL(1,𝔽32) |
| Fitting | C2×C31×C49 | C2×C5 |
| socle | C2×C7×C31 | C5×D7 |
| LCS | G ▷ C31×C49 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3038 |
572 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30380, 17);