Finite Group DatabasebetaFinite Group Databasebeta| order | 18755 |
| automorphism | ? |
| homology | Abelianization (H1) = C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C112×C31 ⋊ C5 |
| Sylow | C112 ⋊ ΓL(1,𝔽32) |
| Sylow | C31 ⋊ #10597243 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C31 | C5 |
| LCS | G ▷ C112×C31 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3751 |
Polycyclic presentation:
5,11^2,31|b^a=b^3,c^a=c^3,d^a=d^4755 conjugacy classes — view the full character table.
| maximal subgroup of | #49175913, #49175919, #49175923, … |
| maximal normal subgroup of | #49175913, #49175919, #49175923, … |
| maximal quotient of | C2×#34037228 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18755, 11);