Finite Group DatabasebetaFinite Group Databasebeta| order | 18386 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×D317 |
| unambiguous semidirect product | C317⋊(C2×C29) |
| Fitting, socle, Hall | C29×C317 ⋊ C2 |
| derived, Sylow | C317 ⋊ C2×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D317 |
| commutator, cosocle, hypocenter | C317 | C2×C29 |
| Frattini | C1 | G |
| Fitting, socle | C29×C317 | C2 |
| LCS | G ▷ C317 | |
| UCS | C1 ◁ C29 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9193 |
4640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C29×#11929639, #49145345, D29×D317, … |
| maximal normal subgroup of | C29×#11929639, #49145345, D29×D317, … |
| maximal quotient of | C29×Dic317, C2×C29×D317 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18386, 2);