Finite Group DatabasebetaFinite Group Databasebeta| order | 10556 |
| automorphism | Aut(G) order 10640448 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2639 |
| unambiguous semidirect product | C7⋊Dic377 |
| derived, Hall | C7×C13×C29 ⋊ C4 |
| Hall | C13×C29 ⋊ Dic7 |
| Hall | C7×C29 ⋊ Dic13 |
| Hall | C7×C13 ⋊ Dic29 |
| Sylow | C29 ⋊ Dic91 |
| Sylow | C13 ⋊ Dic203 |
| Sylow | C7 ⋊ Dic377 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2639 |
| commutator, hypocenter | C7×C13×C29 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C7×C13×C29 | C2 |
| LCS | G ▷ C7×C13×C29 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,13,29,2|a^2=e,b^a=b^6,c^a=c^12,d^a=d^282642 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2639, Dic7917, #44539759, … |
| maximal normal subgroup of | C3×Dic2639, #44539759, ΓL(1,𝔽8)⋊Dic377, … |
| maximal quotient of | C3×Dic2639, Dic7917, Dic13195 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10556, 9);