Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C27)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×((C3⋊D3)⋊C27)⋊C2 |
| unambiguous semidirect product | ((C3⋊D3)⋊C27)⋊C22 |
| unambiguous semidirect product | #92172⋊C22 |
| unambiguous semidirect product | #92206⋊C22 |
| Fitting | C2×C32⋊C27 ⋊ C22 |
| derived, Sylow | C32⋊C27 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | ((C3⋊D3)⋊C27)⋊C2 |
| commutator, cosocle, hypocenter | C32⋊C27 | C23 |
| Frattini | C3×C9 | C2×D32 |
| Fitting | C2×C32⋊C27 | C22 |
| socle | C2×C32 | D3×D9 |
| LCS | G ▷ C32⋊C27 | |
| UCS | C1 ◁ C2 | |
290 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221850 |
| maximal normal subgroup of | C2×#72221850 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 948);