Finite Group DatabasebetaFinite Group Databasebeta| order | 18802 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D553 |
| unambiguous semidirect product | C7⋊(C17×D79) |
| unambiguous semidirect product | C79⋊(D7×C17) |
| Fitting, socle, Hall | C7×C17×C79 ⋊ C2 |
| derived, Hall | C7×C79 ⋊ C2×C17 |
| Hall | C17×C79 ⋊ D7 |
| Hall | C7×C17 ⋊ D79 |
| Sylow | C79 ⋊ D7×C17 |
| Sylow | C7 ⋊ C17×D79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D553 |
| commutator, cosocle, hypocenter | C7×C79 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C7×C17×C79 | C2 |
| LCS | G ▷ C7×C79 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9401 |
4726 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C17×D79, D17×D553, D119⋊D79, … |
| maximal normal subgroup of | D7×C17×D79, D17×D553, D119⋊D79, … |
| maximal quotient of | C17×Dic553, C2×C17×D553 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18802, 6);