Finite Group DatabasebetaFinite Group Databasebeta| order | 9204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C13×C59 ⋊ C22×C3 |
| Hall | D13×D59 ⋊ C3 |
| Hall | C13⋊C3×C59 ⋊ C22 |
| Sylow | C59 ⋊ C2×D13⋊C3 |
| Hall | C13⋊C3 ⋊ C2×D59 |
| Sylow | C13 ⋊ C2×C3×D59 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C59 | C22×C3 |
| LCS | G ▷ C13×C59 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
248 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D13⋊C3×D59, D59×C3⋊(D13⋊C3), D13⋊C3×D177, … |
| maximal normal subgroup of | C3×D13⋊C3×D59 |
| maximal quotient of | D59×D13⋊C9, C3×D13⋊C3×D59, D59×C3⋊(D13⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9204, 16);