Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #92314 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×#92314 |
| Fitting | C22×#6900 ⋊ C2 |
| derived | C92 ⋊ C23×C3 |
| Sylow | #6900 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #92314 |
| commutator, cosocle, hypocenter | C92 | C23×C3 |
| Frattini | C32 | C22×C3×C3⋊D3 |
| Fitting | C22×#6900 | C2 |
| socle | C22×C32 | C3×C3⋊D3 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C22 | |
796 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #72213202, C2×C4×#92314, D4×#92314, … |
| maximal normal subgroup of | #72213202, C2×C4×#92314, D4×#92314, … |
| maximal quotient of | C2×C4×#92314, D4×#92314, C2×C4⋊#92314, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2915);