Finite Group DatabasebetaFinite Group Databasebeta| order | 9204 |
| isoclinism | isoclinic class of D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×Dic39 |
| unambiguous semidirect product | C3⋊(Dic13×C59) |
| derived, Hall | C3×C13 ⋊ C4×C59 |
| Hall | C3×C13×C59 ⋊ C4 |
| Hall | C13×C59 ⋊ Dic3 |
| Hall | C3×C59 ⋊ Dic13 |
| Sylow | C13 ⋊ Dic3×C59 |
| Sylow | C3 ⋊ Dic13×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C59 | D39 |
| commutator, hypocenter | C3×C13 | C4×C59 |
| Frattini | C2 | C59×D39 |
| Fitting, socle | C2×C3×C13×C59 | C2 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C2×C59 | |
24 conjugacy classes of subgroups.
2478 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C59×Dic117, C59×C3⋊(Dic13⋊C3), C59×C3⋊Dic39, … |
| maximal normal subgroup of | C59×C3⋊(Dic13⋊C3), C3×C59×Dic39 |
| maximal quotient of | C59×Dic117, C59×C3⋊Dic39, C3×C59×Dic39 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9204, 8);