Finite Group DatabasebetaFinite Group Databasebeta| order | 27180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C151⋊C9)⋊Dic5 |
| unambiguous semidirect product | Dic755⋊C9 |
| derived, Hall | C5×C151 ⋊ C4×C9 |
| Hall | C5×C151⋊C9 ⋊ C4 |
| Hall | Dic755 ⋊ C9 |
| Hall | C151⋊C9 ⋊ Dic5 |
| Sylow | C151 ⋊ C9×Dic5 |
| Sylow | C5 ⋊ Dic151⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C5⋊(D151⋊C3) |
| commutator, hypocenter | C5×C151 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C151 | C2×C3 |
| LCS | G ▷ C5×C151 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27180 |
Polycyclic presentation:
2,3,5,151,2,3|a^2=e,b^3=f,c^a=c^4,d^a=d^150,d^b=d^32822 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27180, 17);