Finite Group DatabasebetaFinite Group Databasebeta| order | 18585 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9×C59 · Schur multiplier (H2) = C1 |
| derived, Sylow | C7 ⋊ C5×C9×C59 |
| Hall | C5×C7×C59 ⋊ C9 |
| Hall | C7×C59 ⋊ C5×C9 |
| Hall | C5×C7 ⋊ C9×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C59 | ΓL(1,𝔽8) |
| commutator, hypocenter | C7 | C5×C9×C59 |
| Frattini | C3 | C5×ΓL(1,𝔽8)×C59 |
| Fitting, socle, prime radical | C3×C5×C7×C59 | C3 |
| cosocle | C3×C7 | C3×C5×C59 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C3×C5×C59 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18585 |
4425 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×C59×C7⋊C9, C5×C7⋊C9×D59, C5×C59×D7⋊C9, … |
| maximal normal subgroup of | C2×C5×C59×C7⋊C9, C5×C7⋊C9×D59, C5×C59×D7⋊C9, … |
| maximal quotient of | C2×C5×C59×C7⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18585, 2);