Finite Group DatabasebetaFinite Group Databasebeta| order | 10412 |
| automorphism | Aut(G) order 12744288 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2603 |
| unambiguous semidirect product | C19⋊Dic137 |
| derived, Hall | C19×C137 ⋊ C4 |
| Sylow | C137 ⋊ Dic19 |
| Sylow | C19 ⋊ Dic137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2603 |
| commutator, hypocenter | C19×C137 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C19×C137 | C2 |
| LCS | G ▷ C19×C137 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,19,137,2|a^2=d,b^a=b^18,c^a=c^1362606 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2603, Dic7809, (C19⋊C3)⋊Dic137, … |
| maximal normal subgroup of | C3×Dic2603, (C19⋊C3)⋊Dic137, Dic5206 |
| maximal quotient of | C3×Dic2603, Dic7809, Dic13015 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10412, 4);