Finite Group DatabasebetaFinite Group Databasebeta| order | 7436 |
| automorphism | Aut(G) order 5800080 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1859 |
| unambiguous semidirect product | C11⋊Dic169 |
| derived, Hall | C11×C169 ⋊ C4 |
| Sylow | C169 ⋊ Dic11 |
| Sylow | C11 ⋊ Dic169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1859 |
| commutator, hypocenter | C11×C169 | C4 |
| Frattini | C2×C13 | D143 |
| Fitting | C2×C11×C169 | C2 |
| socle | C2×C11×C13 | D13 |
| LCS | G ▷ C11×C169 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,13,2,13|a^2=d,c^13=e^12,b^a=b^10,c^a=c^12e,e^a=e^121862 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11⋊(Dic169⋊C3), C3×Dic1859, Dic5577, … |
| maximal normal subgroup of | C11⋊(Dic169⋊C3), C3×Dic1859, (C11⋊C5)⋊Dic169, … |
| maximal quotient of | C3×Dic1859, Dic5577, C5×Dic1859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7436, 4);