Finite Group DatabasebetaFinite Group Databasebeta| order | 18910 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊D61 |
| Fitting, socle, derived, Hall | C31×C61 ⋊ C2×C5 |
| Hall | C61×ΓL(1,𝔽32) ⋊ C2 |
| Hall | D1891 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ D61 |
| Sylow | C61 ⋊ D31⋊C5 |
| Sylow | C31 ⋊ C5×D61 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C61 | C2×C5 |
| LCS | G ▷ C31×C61 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1891 |
Polycyclic presentation:
2,5,31,61|c^a=c^30,d^a=d^60,c^b=c^16343 conjugacy classes — view the full character table.
| maximal subgroup of | D61×D31⋊C5, C2×ΓL(1,𝔽32)⋊D61 |
| maximal normal subgroup of | D61×D31⋊C5, C2×ΓL(1,𝔽32)⋊D61 |
| maximal quotient of | ΓL(1,𝔽32)⋊Dic61, C2×ΓL(1,𝔽32)⋊D61 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18910, 28);