Finite Group DatabasebetaFinite Group Databasebeta| order | 30380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C7 |
| direct product | C2×C7⋊D7×ΓL(1,𝔽32) |
| unambiguous semidirect product | (C2×C7)⋊(D7×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C2×C31×C7⋊D7)⋊C5 |
| Fitting, socle | C2×C72×C31 ⋊ C2×C5 |
| derived, Hall | C72×C31 ⋊ C22×C5 |
| Hall | C72×ΓL(1,𝔽32) ⋊ C22 |
| Hall | C2×C31×C7⋊D7 ⋊ C5 |
| Sylow | C72 ⋊ C22×ΓL(1,𝔽32) |
| Sylow | C31 ⋊ C2×C5×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C7⋊D7×ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C72×C31 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C31 | C2×C5 |
| LCS | G ▷ C72×C31 | |
| UCS | C1 ◁ C2 | |
200 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, 67);