Finite Group DatabasebetaFinite Group Databasebeta| order | 30380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊Dic1085 |
| unambiguous semidirect product | C31⋊(C7⋊Dic35) |
| derived, Hall | C5×C72×C31 ⋊ C4 |
| Hall | C72×C31 ⋊ Dic5 |
| Hall | C5×C72 ⋊ Dic31 |
| Hall | C5×C31 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ Dic155 |
| Sylow | C31 ⋊ C7⋊Dic35 |
| Sylow | C5 ⋊ C7⋊Dic217 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(C7⋊D217) |
| commutator, hypocenter | C5×C72×C31 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C5×C72×C31 | C2 |
| LCS | G ▷ C5×C72×C31 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 30380 |
Polycyclic presentation:
2,5,7^2,31,2|a^2=f,b^a=b^4,c^a=c^6,d^a=d^6,e^a=e^307598 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30380, 44);