Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #1088 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C3 |
| direct product | C32×#6188 |
| derived | H(3,𝔽3) ⋊ C32×C8 |
| Sylow | C32×H(3,𝔽3) ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C33 | #157 |
| commutator, hypocenter | H(3,𝔽3) | C32×C8 |
| Frattini | C2×C3 | C32×#157 |
| Fitting, prime radical | C2×C32×H(3,𝔽3) | C4 |
| cosocle | #1084 | C2×C32 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C2×C33 | |
456 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2979);