Finite Group DatabasebetaFinite Group Databasebeta| order | 30380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C7⋊D7)⋊(D31⋊C5) |
| unambiguous semidirect product | (C7⋊(D31⋊C5))⋊D7 |
| unambiguous semidirect product | ((C7⋊D7)⋊D31)⋊C5 |
| Fitting, socle, derived, Hall | C72×C31 ⋊ C22×C5 |
| Hall | C72×ΓL(1,𝔽32) ⋊ C22 |
| Hall | (C7⋊D7)⋊D31 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ D72 |
| Sylow | C72 ⋊ C2×D31⋊C5 |
| 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 |
Polycyclic presentation:
2^2,5,7^2,31|d^a=d^6,f^a=f^30,d^b=d^6,e^b=e^6,f^c=f^16203 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30380, 60);