Finite Group DatabasebetaFinite Group Databasebeta| order | 27474 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C19×C241 ⋊ C2×C3 |
| Hall | #28351596 ⋊ C2 |
| Hall | D19×C241 ⋊ C3 |
| Sylow | C241 ⋊ D19⋊C3 |
| Hall | D19 ⋊ C241⋊C3 |
| Sylow | C19 ⋊ C2×C241⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C241 | C2×C3 |
| LCS | G ▷ C19×C241 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4579 |
Polycyclic presentation:
2,3,19,241|c^a=c^18,c^b=c^7,d^b=d^225889 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27474, 20);