Finite Group DatabasebetaFinite Group Databasebeta| order | 30380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊(C7⋊(Dic31⋊C5)) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊(C7⋊Dic7) |
| unambiguous semidirect product | (C7⋊Dic217)⋊C5 |
| derived, Hall | C72×C31 ⋊ C4×C5 |
| Hall | C72×ΓL(1,𝔽32) ⋊ C4 |
| Hall | C7⋊Dic217 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ Dic31⋊C5 |
| Sylow | C31 ⋊ C5×C7⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊(C7⋊(D31⋊C5)) |
| commutator, hypocenter | C72×C31 | C4×C5 |
| Fitting, socle, cosocle | C2×C72×C31 | C2×C5 |
| prime radical | C2×C72×ΓL(1,𝔽32) | C2 |
| LCS | G ▷ C72×C31 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6076 |
Polycyclic presentation:
2,5,7^2,31,2|a^2=f,c^a=c^6,d^a=d^6,e^a=e^30,e^b=e^16554 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30380, 41);