Finite Group DatabasebetaFinite Group Databasebeta| order | 17745 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C5×C132 ⋊ C3×C7 |
| derived, Sylow | C132 ⋊ C3×C5×C7 |
| Hall | C5×C132⋊C7 ⋊ C3 |
| Hall | C5×#92788 ⋊ C7 |
| Hall | C132⋊C7 ⋊ C3×C5 |
| Hall | #92788 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #92788⋊C7 |
| commutator, cosocle, hypocenter | C132 | C3×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C132 | C3×C7 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 455 |
145 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#14556975⋊C3, C5×#11759815⋊C7, D5×#92788⋊C7, … |
| maximal normal subgroup of | C5×#14556975⋊C3, C5×#11759815⋊C7, D5×#92788⋊C7, … |
| maximal quotient of | C2×C5×#92788⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17745, 7);