Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | H(3,𝔽3)×#625 |
| unambiguous semidirect product | (C32×#625)⋊C3 |
| Sylow | C32×H(3,𝔽3) ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C3 | C32×D32 |
| commutator, socle, cosocle | C2×C33 | C22×C32 |
| Fitting | C2×C32×H(3,𝔽3) | C22 |
| hypercenter | C2×H(3,𝔽3) | D32 |
| hypocenter | C32 | D4×H(3,𝔽3) |
| LCS | G ▷ C2×C33 ▷ C32 | |
| UCS | C1 ◁ C2×C3 ◁ C2×H(3,𝔽3) | |
849 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 849 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3023);