Finite Group DatabasebetaFinite Group Databasebeta| order | 18802 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17×C79 · Schur multiplier (H2) = C1 |
| direct product | D7×C17×C79 |
| unambiguous semidirect product | C7⋊(C2×C17×C79) |
| Fitting, socle, Hall | C7×C17×C79 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C17×C79 |
| Hall | C7×C79 ⋊ C2×C17 |
| Hall | C7×C17 ⋊ C2×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17×C79 | D7 |
| commutator, cosocle, hypocenter | C7 | C2×C17×C79 |
| Frattini | C1 | G |
| Fitting, socle | C7×C17×C79 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C17×C79 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9401 |
6715 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C17×D79, D7×D17×C79, D7×D1343, … |
| maximal normal subgroup of | D7×C17×D79, D7×D17×C79, D7×D1343, … |
| maximal quotient of | C17×Dic7×C79, C2×D7×C17×C79 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18802, 5);