Finite Group DatabasebetaFinite Group Databasebeta| order | 18755 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C112 · Schur multiplier (H2) = C11 |
| direct product | C112×ΓL(1,𝔽32) |
| unambiguous semidirect product | C31⋊(C5×C112) |
| Fitting, socle, Hall | C112×C31 ⋊ C5 |
| derived, Sylow | C31 ⋊ C5×C112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C112 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C5×C112 |
| Frattini | C1 | G |
| Fitting, socle | C112×C31 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C112 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3751 |
1331 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C112×D31⋊C5, C11×ΓL(1,𝔽32)⋊D11, C11×D11×ΓL(1,𝔽32), … |
| maximal normal subgroup of | C112×D31⋊C5, C11×ΓL(1,𝔽32)⋊D11, C11×D11×ΓL(1,𝔽32), … |
| maximal quotient of | C2×C112×ΓL(1,𝔽32) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18755, 27);