Finite Group DatabasebetaFinite Group Databasebeta| order | 5148 |
| automorphism | Aut(G) order 1853280 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1287 |
| unambiguous semidirect product | C9⋊Dic143 |
| unambiguous semidirect product | C11⋊Dic117 |
| derived, Hall | C9×C11×C13 ⋊ C4 |
| Hall | C11×C13 ⋊ Dic9 |
| Hall | C9×C13 ⋊ Dic11 |
| Hall | C9×C11 ⋊ Dic13 |
| Sylow | C13 ⋊ Dic99 |
| Sylow | C11 ⋊ Dic117 |
| Sylow | C9 ⋊ Dic143 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1287 |
| commutator, hypocenter | C9×C11×C13 | C4 |
| Frattini | C2×C3 | D429 |
| Fitting | C2×C9×C11×C13 | C2 |
| socle | C2×C3×C11×C13 | D3 |
| LCS | G ▷ C9×C11×C13 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,11,13,2,3|a^2=e,b^3=f^2,b^a=b^2f,c^a=c^10,d^a=d^12,f^a=f^21290 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×Dic1287, Dic6435, C9⋊((C11⋊C5)⋊Dic13), … |
| maximal normal subgroup of | C5×Dic1287, C9⋊((C11⋊C5)⋊Dic13), C7×Dic1287, … |
| maximal quotient of | C5×Dic1287, Dic6435, C9⋊(C11⋊#63120), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5148, 12);