Finite Group DatabasebetaFinite Group Databasebeta| order | 4972 |
| automorphism | Aut(G) order 2784320 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1243 |
| unambiguous semidirect product | C11⋊Dic113 |
| derived, Hall | C11×C113 ⋊ C4 |
| Sylow | C113 ⋊ Dic11 |
| Sylow | C11 ⋊ Dic113 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1243 |
| commutator, hypocenter | C11×C113 | C4 |
| Fitting, socle | C2×C11×C113 | C2 |
| LCS | G ▷ C11×C113 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,11,113,2|a^2=d,b^a=b^10,c^a=c^1121246 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic1243, Dic3729, C5×Dic1243, … |
| maximal normal subgroup of | C3×Dic1243, C5×Dic1243, (C11⋊C5)⋊Dic113, … |
| maximal quotient of | C3×Dic1243, Dic3729, C5×Dic1243, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4972, 4);