Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #1113⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3×#1113⋊C3 |
| unambiguous semidirect product | (C2×#1113)⋊C32 |
| unambiguous semidirect product | (C2×C3×#1113)⋊C3 |
| Fitting, socle | C2×C34 ⋊ A4 |
| derived | #1113 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #1113⋊C3 |
| commutator, cosocle, hypocenter | #1113 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C34 | A4 |
| LCS | G ▷ #1113 | |
| UCS | C1 ◁ C2×C3 | |
290 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3883);