Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊(C3⋊D27) |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C33 |
| direct product | C22×C3⋊(C3⋊D27) |
| Fitting | C22×C32×C27 ⋊ C2 |
| derived, Sylow | C32×C27 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C3⋊(C3⋊D27) |
| commutator, cosocle, hypocenter | C32×C27 | C23 |
| Frattini | C9 | C22×C3⋊(C3⋊D3) |
| Fitting | C22×C32×C27 | C2 |
| socle | C22×C33 | D9 |
| LCS | G ▷ C32×C27 | |
| UCS | C1 ◁ C22 | |
1152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 972 |
492 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2940);