Finite Group DatabasebetaFinite Group Databasebeta| order | 1872 |
| isoclinism | isoclinic class of C3⋊(D13⋊A4) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×C3⋊(D13⋊A4) |
| unambiguous semidirect product | (C2×C3)⋊(D13⋊A4) |
| unambiguous semidirect product | (C2×D39)⋊A4 |
| unambiguous semidirect product | (C2×C22⋊(C13⋊C3))⋊D3 |
| Fitting, socle | C23×C3×C13 ⋊ C2×C3 |
| derived | C22×C3×C13 ⋊ C22×C3 |
| Sylow | C13 ⋊ C2×D3×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(D13⋊A4) |
| commutator, cosocle, hypocenter | C22×C3×C13 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C23×C3×C13 | C2×C3 |
| LCS | G ▷ C22×C3×C13 | |
| UCS | C1 ◁ C2 | |
164 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 234 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1872, 1074);