Finite Group DatabasebetaFinite Group Databasebeta| order | 18369 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C13×C157 ⋊ C9 |
| Sylow | C157 ⋊ C13⋊C9 |
| Sylow | C13 ⋊ C157⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #20259404 |
| commutator, hypocenter | C13×C157 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C13×C157 | C3 |
| LCS | G ▷ C13×C157 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18369 |
Polycyclic presentation:
3,13,157,3|a^3=d,b^a=b^3,c^a=c^122049 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#32913541, #49144997, #49145001, … |
| maximal normal subgroup of | C2×#32913541, #49144997, #49145001, … |
| maximal quotient of | C2×#32913541 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18369, 6);