Finite Group DatabasebetaFinite Group Databasebeta| order | 8940 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#15688382 |
| Fitting, socle, derived, Hall | C3×C5×C149 ⋊ C4 |
| Hall | C5×C149 ⋊ Dic3 |
| Hall | C3×C149 ⋊ AGL(1,𝔽5) |
| Sylow | C149 ⋊ ΓL(1,𝔽16) |
| Hall | C3×C5 ⋊ #10597010 |
| Sylow | C5 ⋊ C3⋊#10597010 |
| Sylow | C3 ⋊ #15688382 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C149 | C4 |
| LCS | G ▷ C3×C5×C149 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,149|a^2=b,c^a=c^2,d^a=d^2,e^a=e^44,d^b=d^4,e^b=e^148564 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊#15688382, C3×C3⋊#15688382, C3⋊(C3⋊#15688382) |
| maximal normal subgroup of | C3×C3⋊#15688382 |
| maximal quotient of | C9⋊#15688382, C3×C3⋊#15688382, C3⋊(C3⋊#15688382) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8940, 21);