Finite Group DatabasebetaFinite Group Databasebeta| order | 9546 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#18012030 |
| Fitting, socle, Hall | C2×C37×C43 ⋊ C3 |
| derived, Hall | C37×C43 ⋊ C2×C3 |
| Hall | C2×C43 ⋊ C37⋊C3 |
| Hall | C2×C37 ⋊ C43⋊C3 |
| Sylow | C43 ⋊ C2×C37⋊C3 |
| Sylow | C37 ⋊ C2×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #18012030 |
| commutator, cosocle, hypocenter | C37×C43 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C37×C43 | C3 |
| LCS | G ▷ C37×C43 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
1066 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#18012030, #34061843, #34061847, … |
| maximal normal subgroup of | C4×#18012030, #34061843, #34061847, … |
| maximal quotient of | C4×#18012030, C22×#18012030, C2×#28384886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9546, 4);