Finite Group DatabasebetaFinite Group Databasebeta| order | 8940 |
| automorphism | Aut(G) order 5292480 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2235 |
| unambiguous semidirect product | C3⋊Dic745 |
| derived, Hall | C3×C5×C149 ⋊ C4 |
| Hall | C5×C149 ⋊ Dic3 |
| Hall | C3×C149 ⋊ Dic5 |
| Sylow | C149 ⋊ Dic15 |
| Hall | C3×C5 ⋊ Dic149 |
| Sylow | C5 ⋊ Dic447 |
| Sylow | C3 ⋊ Dic745 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2235 |
| commutator, hypocenter | C3×C5×C149 | C4 |
| Fitting, socle | C2×C3×C5×C149 | C2 |
| LCS | G ▷ C3×C5×C149 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,149,2|a^2=e,b^a=b^2,c^a=c^4,d^a=d^1482238 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic6705, C3⋊Dic2235, C3×Dic2235, … |
| maximal normal subgroup of | C3×Dic2235, Dic4470 |
| maximal quotient of | Dic6705, C3⋊Dic2235, C3×Dic2235, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8940, 8);