Finite Group DatabasebetaFinite Group Databasebeta| order | 18755 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×#13133724 |
| Fitting, socle, Hall | C112×C31 ⋊ C5 |
| derived | C11×C31 ⋊ C5×C11 |
| Sylow | C112 ⋊ ΓL(1,𝔽32) |
| Sylow | C31 ⋊ C11×C11⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | #13133724 |
| commutator, cosocle, hypocenter | C11×C31 | C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C112×C31 | C5 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C11 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1705 |
803 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#16811774, C11×#16811786, C11×#16811780, … |
| maximal normal subgroup of | C11×#16811774, C11×#16811786, C11×#16811780, … |
| maximal quotient of | C2×C11×#13133724 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18755, 15);