Finite Group DatabasebetaFinite Group Databasebeta| order | 10716 |
| automorphism | Aut(G) order 8872848 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2679 |
| unambiguous semidirect product | C3⋊Dic893 |
| unambiguous semidirect product | C19⋊Dic141 |
| unambiguous semidirect product | C47⋊Dic57 |
| derived, Hall | C3×C19×C47 ⋊ C4 |
| Hall | C19×C47 ⋊ Dic3 |
| Hall | C3×C47 ⋊ Dic19 |
| Hall | C3×C19 ⋊ Dic47 |
| Sylow | C47 ⋊ Dic57 |
| Sylow | C19 ⋊ Dic141 |
| Sylow | C3 ⋊ Dic893 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2679 |
| commutator, hypocenter | C3×C19×C47 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C19×C47 | C2 |
| LCS | G ▷ C3×C19×C47 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,19,47,2|a^2=e,b^a=b^2,c^a=c^18,d^a=d^462682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic8037, C3⋊(C47⋊((C19⋊C3)⋊C4)), C3⋊Dic2679, … |
| maximal normal subgroup of | C3⋊(C47⋊((C19⋊C3)⋊C4)), C3×Dic2679, Dic5358 |
| maximal quotient of | Dic8037, C3⋊Dic2679, C3×Dic2679, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10716, 9);