Finite Group DatabasebetaFinite Group Databasebeta| order | 9243 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C79⋊C9)⋊C13 |
| unambiguous semidirect product | (C79⋊C13)⋊C9 |
| derived, Sylow | C79 ⋊ C9×C13 |
| Hall | C79⋊C13 ⋊ C9 |
| Hall | C79⋊C9 ⋊ C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C79⋊C3)⋊C13 |
| commutator, hypocenter | C79 | C9×C13 |
| Fitting, socle | C3×C79 | C3×C13 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
3,13,79,3|a^3=d,c^a=c^23,c^b=c^18123 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C79⋊C9)⋊C13, (D79⋊C9)⋊C13, C22⋊((C79⋊C9)⋊C13) |
| maximal normal subgroup of | C2×(C79⋊C9)⋊C13, (D79⋊C9)⋊C13 |
| maximal quotient of | C2×(C79⋊C9)⋊C13, C22⋊((C79⋊C9)⋊C13) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9243, 2);