Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C35 |
| direct product | C22×#92404 |
| Fitting | C22×H(5,𝔽3) ⋊ C2 |
| derived, Sylow | H(5,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C22×C3 | C3⋊(C3⋊(C3⋊D3)) |
| commutator, cosocle, hypocenter | H(5,𝔽3) | C23 |
| Frattini | C3 | C22×C3⋊(C3⋊(C3⋊D3)) |
| Fitting | C22×H(5,𝔽3) | C2 |
| LCS | G ▷ H(5,𝔽3) | |
| UCS | C1 ◁ C22×C3 | |
4688 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
184 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#11758086 |
| maximal normal subgroup of | C22×#11758086 |
| maximal quotient of | C22×#13091502 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3775);