Finite Group DatabasebetaFinite Group Databasebeta| order | 30070 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C97 · Schur multiplier (H2) = C1 |
| direct product | C97×D31⋊C5 |
| unambiguous semidirect product | D31⋊(C5×C97) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊(C2×C97) |
| unambiguous semidirect product | (D31×C97)⋊C5 |
| Fitting, socle, Hall | C31×C97 ⋊ C2×C5 |
| derived, Sylow | C31 ⋊ C2×C5×C97 |
| Hall | C97×ΓL(1,𝔽32) ⋊ C2 |
| Hall | D31×C97 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C2×C97 |
| Hall | D31 ⋊ C5×C97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C97 | D31⋊C5 |
| commutator, cosocle, hypocenter | C31 | C2×C5×C97 |
| Frattini | C1 | G |
| Fitting, socle | C31×C97 | C2×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C97 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3007 |
1261 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30070, 11);