Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #157⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×#157⋊D3 |
| unambiguous semidirect product | #157⋊(C32×D3) |
| Fitting, socle, Sylow | C35 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #157⋊D3 |
| commutator, cosocle | C3×C3⋊D3 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C35 | D4 |
| hypocenter | C33 | C32×D4 |
| LCS | G ▷ C3×C3⋊D3 ▷ C33 | |
| UCS | C1 ◁ C32 | |
884 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | C3×(#157⋊D3)⋊D3, C3×D3×#157⋊D3, #72228531 |
| maximal normal subgroup of | C3×(#157⋊D3)⋊D3, C3×D3×#157⋊D3, #72228531 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3909);