Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #92391 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C4 · Schur multiplier (H2) = C2×C32 |
| direct product | C4×#92391 |
| Fitting | C4×H(5,𝔽3) ⋊ C2 |
| derived | C33 ⋊ C2×C32×C4 |
| Sylow | H(5,𝔽3) ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #92391 |
| commutator, hypocenter | C33 | C2×C32×C4 |
| Frattini, socle | C2×C3 | C2×C32×C3⋊D3 |
| Fitting | C4×H(5,𝔽3) | C2 |
| prime radical | C2×#92391 | C2 |
| cosocle | C2×C33 | C22×C32 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C4 | |
771 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 771 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3330);