Finite Group DatabasebetaFinite Group Databasebeta| order | 30380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C7⋊D7)⋊D155 |
| Fitting, socle, derived, Hall | C5×C72×C31 ⋊ C22 |
| Hall | C72×C31 ⋊ C2×D5 |
| Hall | C5×C72 ⋊ C2×D31 |
| Hall | C5×C31 ⋊ D72 |
| Sylow | C72 ⋊ C2×D155 |
| Sylow | C31 ⋊ D35⋊D7 |
| Sylow | C5 ⋊ (C7⋊D7)⋊D31 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C72×C31 | C22 |
| LCS | G ▷ C5×C72×C31 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2170 |
Polycyclic presentation:
2^2,5,7^2,31|c^a=c^4,d^a=d^6,f^a=f^30,d^b=d^6,e^b=e^62027 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30380, 97);