Finite Group DatabasebetaFinite Group Databasebeta| order | 17545 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×#10597243 |
| Fitting, socle, Hall | C112×C29 ⋊ C5 |
| derived, Sylow | C112 ⋊ C5×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | #10597243 |
| commutator, cosocle, hypocenter | C112 | C5×C29 |
| Frattini | C1 | G |
| Fitting, socle | C112×C29 | C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C29 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3509 |
841 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D29×#10597243, C29×#11925892, C29⋊#11925892, … |
| maximal normal subgroup of | D29×#10597243, C29×#11925892, C29⋊#11925892, … |
| maximal quotient of | C2×C29×#10597243 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17545, 4);