Finite Group DatabasebetaFinite Group Databasebeta| order | 30380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | D72×ΓL(1,𝔽32) |
| unambiguous semidirect product | (C7×D7)⋊(C2×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C7⋊D7)⋊(C2×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (D72×C31)⋊C5 |
| Fitting, socle, derived, Hall | C72×C31 ⋊ C22×C5 |
| Hall | C72×ΓL(1,𝔽32) ⋊ C22 |
| Hall | D72×C31 ⋊ C5 |
| Sylow | C72 ⋊ C22×ΓL(1,𝔽32) |
| Sylow | C31 ⋊ C5×D72 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C31 | C22×C5 |
| LCS | G ▷ C72×C31 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 434 |
275 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30380, 61);