Finite Group DatabasebetaFinite Group Databasebeta| order | 18386 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C317 · Schur multiplier (H2) = C1 |
| direct product | D29×C317 |
| unambiguous semidirect product | C29⋊(C2×C317) |
| Fitting, socle, Hall | C29×C317 ⋊ C2 |
| derived, Sylow | C29 ⋊ C2×C317 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C317 | D29 |
| commutator, cosocle, hypocenter | C29 | C2×C317 |
| Frattini | C1 | G |
| Fitting, socle | C29×C317 | C2 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C317 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9193 |
5072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1181×C317, #49145344, D29×D317, … |
| maximal normal subgroup of | #1181×C317, #49145344, D29×D317, … |
| maximal quotient of | Dic29×C317, C2×D29×C317 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18386, 1);