Finite Group DatabasebetaFinite Group Databasebeta| order | 30420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C5×C132 ⋊ C4×C9 |
| Hall | C5×C13×C13⋊C9 ⋊ C4 |
| Hall | #16809991 ⋊ C9 |
| Hall | C13×C13⋊C9 ⋊ Dic5 |
| Sylow | C132 ⋊ C9×Dic5 |
| Sylow | C5 ⋊ #20258756 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C5⋊((C13⋊C3)⋊D13) |
| commutator, hypocenter | C5×C132 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C132 | C2×C3 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 ◁ C2×C3 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2340 |
Polycyclic presentation:
2,3,5,13^2,2,3|a^2=f,b^3=g,c^a=c^4,d^a=d^12,e^a=e^12,d^b=d^31392 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 181);