Finite Group DatabasebetaFinite Group Databasebeta| order | 7340 |
| automorphism | Aut(G) order 5372880 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1835 |
| unambiguous semidirect product | C367⋊Dic5 |
| derived, Hall | C5×C367 ⋊ C4 |
| Sylow | C367 ⋊ Dic5 |
| Sylow | C5 ⋊ Dic367 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1835 |
| commutator, hypocenter | C5×C367 | C4 |
| Fitting, socle | C2×C5×C367 | C2 |
| LCS | G ▷ C5×C367 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,367,2|a^2=d,b^a=b^4,c^a=c^3661838 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic1835, Dic5505, (C367⋊C3)⋊Dic5, … |
| maximal normal subgroup of | C3×Dic1835, (C367⋊C3)⋊Dic5, C5×Dic1835, … |
| maximal quotient of | C3×Dic1835, Dic5505, Dic9175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7340, 4);