Finite Group DatabasebetaFinite Group Databasebeta| order | 9204 |
| automorphism | Aut(G) order 6405984 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4602 |
| direct product | C2×D2301 |
| unambiguous semidirect product | (C2×C3)⋊D767 |
| unambiguous semidirect product | (C2×C13)⋊D177 |
| unambiguous semidirect product | (C2×C59)⋊D39 |
| Fitting, socle | C2×C3×C13×C59 ⋊ C2 |
| derived, Hall | C3×C13×C59 ⋊ C22 |
| Hall | C13×C59 ⋊ C2×D3 |
| Hall | C3×C59 ⋊ C2×D13 |
| Sylow | C59 ⋊ C2×D39 |
| Hall | C3×C13 ⋊ C2×D59 |
| Sylow | C13 ⋊ C2×D177 |
| Sylow | C3 ⋊ C2×D767 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2301 |
| commutator, hypocenter | C3×C13×C59 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C13×C59 | C2 |
| LCS | G ▷ C3×C13×C59 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
2304 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D6903, C2×C3⋊((C13⋊C3)⋊D59), D3×D2301, … |
| maximal normal subgroup of | C2×C3⋊((C13⋊C3)⋊D59), C2×C3×D2301, D9204 |
| maximal quotient of | C2×D6903, D3×D2301, C2×C3×D2301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9204, 34);