Finite Group DatabasebetaFinite Group Databasebeta| order | 18718 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×D191 |
| unambiguous semidirect product | C191⋊(C2×C49) |
| Fitting, Hall | C49×C191 ⋊ C2 |
| derived, Sylow | C191 ⋊ C2×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | D191 |
| commutator, hypocenter | C191 | C2×C49 |
| Frattini | C7 | C7×D191 |
| Fitting | C49×C191 | C2 |
| socle, cosocle | C7×C191 | C2×C7 |
| prime radical | C7×D191 | C7 |
| LCS | G ▷ C191 | |
| UCS | C1 ◁ C49 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9359 |
4753 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D49×D191, C2×C49×D191 |
| maximal normal subgroup of | D49×D191, C2×C49×D191 |
| maximal quotient of | C49×Dic191, C2×C49×D191 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18718, 3);