Finite Group DatabasebetaFinite Group Databasebeta| order | 8492 |
| automorphism | Aut(G) order 8152320 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2123 |
| unambiguous semidirect product | C11⋊Dic193 |
| derived, Hall | C11×C193 ⋊ C4 |
| Sylow | C193 ⋊ Dic11 |
| Sylow | C11 ⋊ Dic193 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2123 |
| commutator, hypocenter | C11×C193 | C4 |
| Fitting, socle | C2×C11×C193 | C2 |
| LCS | G ▷ C11×C193 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,193,2|a^2=d,b^a=b^10,c^a=c^1922126 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2123, Dic6369, C11⋊(Dic193⋊C3), … |
| maximal normal subgroup of | C3×Dic2123, C11⋊(Dic193⋊C3), Dic4246 |
| maximal quotient of | C3×Dic2123, Dic6369, Dic14861 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8492, 4);