Finite Group DatabasebetaFinite Group Databasebeta| order | 10724 |
| automorphism | Aut(G) order 12289704 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2681 |
| unambiguous semidirect product | C7⋊Dic383 |
| unambiguous semidirect product | C383⋊Dic7 |
| derived, Hall | C7×C383 ⋊ C4 |
| Sylow | C383 ⋊ Dic7 |
| Sylow | C7 ⋊ Dic383 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2681 |
| commutator, hypocenter | C7×C383 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C7×C383 | C2 |
| LCS | G ▷ C7×C383 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,383,2|a^2=d,b^a=b^6,c^a=c^3822684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2681, Dic8043, ΓL(1,𝔽8)⋊Dic383, … |
| maximal normal subgroup of | C3×Dic2681, ΓL(1,𝔽8)⋊Dic383, Dic5362 |
| maximal quotient of | C3×Dic2681, Dic8043, Dic13405 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10724, 4);