Finite Group DatabasebetaFinite Group Databasebeta| order | 18297 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C107 · Schur multiplier (H2) = C1 |
| direct product | C107×#4294 |
| derived, Sylow | C19 ⋊ C9×C107 |
| Hall | C19×C107 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C107 | C19⋊C3 |
| commutator, hypocenter | C19 | C9×C107 |
| Frattini | C3 | C19⋊C3×C107 |
| Fitting, socle, prime radical | C3×C19×C107 | C3 |
| cosocle | C3×C19 | C3×C107 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C107 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18297 |
2889 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C107×#4294, #4294×D107, C107×#4294⋊C2, … |
| maximal normal subgroup of | C2×C107×#4294, #4294×D107, C107×#4294⋊C2, … |
| maximal quotient of | C2×C107×#4294 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18297, 2);