Finite Group DatabasebetaFinite Group Databasebeta| order | 9243 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#15690494 |
| Fitting, socle | C3×C13×C79 ⋊ C3 |
| derived, Hall | C13×C79 ⋊ C32 |
| Sylow | C79 ⋊ C3×C13⋊C3 |
| Sylow | C13 ⋊ C3×C79⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #15690494 |
| commutator, hypocenter | C13×C79 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C79 | C3 |
| LCS | G ▷ C13×C79 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
1035 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#20259722, C3×#20259718, C3×#20259714, … |
| maximal normal subgroup of | C3×#20259722, C3×#20259718, C3×#20259714, … |
| maximal quotient of | C2×C3×#15690494, A4×#15690494, C3×C22⋊#15690494 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9243, 13);