Finite Group DatabasebetaFinite Group Databasebeta| order | 9204 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C59⋊(Dic13⋊C3) |
| unambiguous semidirect product | Dic767⋊C3 |
| derived, Hall | C13×C59 ⋊ C3×C4 |
| Hall | Dic767 ⋊ C3 |
| Hall | C13⋊C3×C59 ⋊ C4 |
| Sylow | C59 ⋊ Dic13⋊C3 |
| Hall | C13⋊C3 ⋊ Dic59 |
| Sylow | C13 ⋊ C3×Dic59 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C13⋊C3)⋊D59 |
| commutator, hypocenter | C13×C59 | C3×C4 |
| Fitting, socle | C2×C13×C59 | C2×C3 |
| LCS | G ▷ C13×C59 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,13,59,2|a^2=e,c^a=c^12,d^a=d^58,c^b=c^3422 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C59⋊(Dic13⋊C3), C3⋊(C59⋊(Dic13⋊C3)) |
| maximal normal subgroup of | C3×C59⋊(Dic13⋊C3) |
| maximal quotient of | C59⋊(Dic13⋊C9), C3×C59⋊(Dic13⋊C3), C3⋊(C59⋊(Dic13⋊C3)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9204, 12);