Finite Group DatabasebetaFinite Group Databasebeta| order | 18717 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×C367⋊C3 |
| unambiguous semidirect product | C367⋊(C3×C17) |
| unambiguous semidirect product | (C17×C367)⋊C3 |
| Fitting, socle, Hall | C17×C367 ⋊ C3 |
| derived, Sylow | C367 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C367⋊C3 |
| commutator, cosocle, hypocenter | C367 | C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C367 | C3 |
| LCS | G ▷ C367 | |
| UCS | C1 ◁ C17 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6239 |
2125 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C17×C367⋊C3, C17×D367⋊C3, D17×C367⋊C3, … |
| maximal normal subgroup of | C2×C17×C367⋊C3, C17×D367⋊C3, D17×C367⋊C3, … |
| maximal quotient of | C2×C17×C367⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18717, 1);