Finite Group DatabasebetaFinite Group Databasebeta| order | 10564 |
| automorphism | Aut(G) order 13120488 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2641 |
| unambiguous semidirect product | C19⋊Dic139 |
| unambiguous semidirect product | C139⋊Dic19 |
| derived, Hall | C19×C139 ⋊ C4 |
| Sylow | C139 ⋊ Dic19 |
| Sylow | C19 ⋊ Dic139 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2641 |
| commutator, hypocenter | C19×C139 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C19×C139 | C2 |
| LCS | G ▷ C19×C139 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,19,139,2|a^2=d,b^a=b^18,c^a=c^1382644 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2641, Dic7923, (C139⋊C3)⋊Dic19, … |
| maximal normal subgroup of | C3×Dic2641, (C139⋊C3)⋊Dic19, (C19⋊C3)⋊Dic139, … |
| maximal quotient of | C3×Dic2641, Dic7923, Dic13205 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10564, 4);