Finite Group DatabasebetaFinite Group Databasebeta| order | 18445 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7×C17 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C7×C17×C31 ⋊ C5 |
| derived, Sylow | C31 ⋊ C5×C7×C17 |
| Hall | C17×C31 ⋊ C5×C7 |
| Hall | C7×C31 ⋊ C5×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C17 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C5×C7×C17 |
| Frattini | C1 | G |
| Fitting, socle | C7×C17×C31 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C7×C17 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3689 |
1309 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C7×C17×ΓL(1,𝔽32), C7×C17×D31⋊C5, C7×D17×ΓL(1,𝔽32), … |
| maximal normal subgroup of | C2×C7×C17×ΓL(1,𝔽32), C7×C17×D31⋊C5, C7×D17×ΓL(1,𝔽32), … |
| maximal quotient of | C2×C7×C17×ΓL(1,𝔽32) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18445, 2);