Finite Group DatabasebetaFinite Group Databasebeta| order | 17745 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#16813075 |
| Fitting, socle, Hall | C5×C7×C132 ⋊ C3 |
| derived, Hall | C7×C132 ⋊ C3×C5 |
| Hall | C5×C132 ⋊ ΓL(1,𝔽8) |
| Sylow | C132 ⋊ C5×ΓL(1,𝔽8) |
| Hall | C5×C7 ⋊ #92788 |
| Sylow | C7 ⋊ C5×#92788 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #16813075 |
| commutator, cosocle, hypocenter | C7×C132 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C132 | C3 |
| LCS | G ▷ C7×C132 | |
| UCS | C1 ◁ C5 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5915 |
1985 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#20296911, C5×#20296902, C5×#20296905, … |
| maximal normal subgroup of | C5×#20296911, C5×#20296902, C5×#20296905, … |
| maximal quotient of | C2×C5×#16813075 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17745, 12);