Finite Group DatabasebetaFinite Group Databasebeta| order | 18755 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C31×C121 ⋊ C5 |
| Sylow | C121 ⋊ ΓL(1,𝔽32) |
| Sylow | C31 ⋊ C121⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C31×C121 | C5 |
| Frattini | C11 | #13133721 |
| socle | C11×C31 | C11⋊C5 |
| LCS | G ▷ C31×C121 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3751 |
Polycyclic presentation:
5,11,31,11|b^11=d,b^a=b^3,c^a=c^2,d^a=d^3755 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#34037221, #49175855, #49175861, … |
| maximal normal subgroup of | C2×#34037221, #49175855, #49175861, … |
| maximal quotient of | C2×#34037221 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18755, 4);