Finite Group DatabasebetaFinite Group Databasebeta| order | 15618 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C137 · Schur multiplier (H2) = C1 |
| direct product | C3×D19×C137 |
| Fitting, socle, Hall | C3×C19×C137 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C3×C137 |
| Hall | C19×C137 ⋊ C2×C3 |
| Hall | C3×C19 ⋊ C2×C137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C137 | D19 |
| commutator, cosocle, hypocenter | C19 | C2×C3×C137 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C137 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C137 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7809 |
4521 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D19×D137, D3×D19×C137, D19×D411, … |
| maximal normal subgroup of | C3×D19×D137, D3×D19×C137, D19×D411, … |
| maximal quotient of | C3×Dic19×C137, C2×C3×D19×C137 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15618, 4);