Finite Group DatabasebetaFinite Group Databasebeta| order | 18369 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#20259404 |
| Fitting, socle | C3×C13×C157 ⋊ C3 |
| derived, Hall | C13×C157 ⋊ C32 |
| Sylow | C157 ⋊ C3×C13⋊C3 |
| Sylow | C13 ⋊ C3×C157⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #20259404 |
| commutator, cosocle, hypocenter | C13×C157 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C157 | C3 |
| LCS | G ▷ C13×C157 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6123 |
2049 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#27133649, C3×#27133645, C3×#27133641, … |
| maximal normal subgroup of | C3×#27133649, C3×#27133645, C3×#27133641, … |
| maximal quotient of | C2×C3×#20259404 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18369, 12);