Finite Group DatabasebetaFinite Group Databasebeta| order | 18718 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×D191 |
| unambiguous semidirect product | C191⋊(C2×C72) |
| Fitting, socle, Hall | C72×C191 ⋊ C2 |
| derived, Sylow | C191 ⋊ C2×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D191 |
| commutator, cosocle, hypocenter | C191 | C2×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C191 | C2 |
| LCS | G ▷ C191 | |
| UCS | C1 ◁ C72 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9359 |
4753 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D7×D191, C7⋊D7×D191, C2×C72×D191 |
| maximal normal subgroup of | C7×D7×D191, C7⋊D7×D191, C2×C72×D191 |
| maximal quotient of | C72×Dic191, C2×C72×D191 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18718, 10);