Finite Group DatabasebetaFinite Group Databasebeta| order | 30380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊#5997 |
| unambiguous semidirect product | (C31⋊#5997)⋊C5 |
| Fitting, socle, derived, Hall | C72×C31 ⋊ C4×C5 |
| Hall | C72×ΓL(1,𝔽32) ⋊ C4 |
| Hall | C31⋊#5997 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ #5997 |
| Sylow | C72 ⋊ Dic31⋊C5 |
| Sylow | C31 ⋊ C5×#5997 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C31 | C4×C5 |
| prime radical | C7⋊D7×ΓL(1,𝔽32) | C2 |
| cosocle | C31×C7⋊D7 | C2×C5 |
| LCS | G ▷ C72×C31 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 434 |
Polycyclic presentation:
2,5,2,7^2,31|a^2=c,d^a=d^4e^3,e^a=d^6e^3,f^a=f^30,f^b=f^16,d^c=d^6,e^c=e^6158 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30380, 56);