Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C33 |
| direct product | C22×C32×C13⋊C3 |
| Fitting, socle | C22×C32×C13 ⋊ C3 |
| derived, Sylow | C13 ⋊ C22×C33 |
| Hall | C22×C13 ⋊ C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C22×C33 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C13 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C22×C32 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 468 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C32×D13⋊C3, C22×C3⋊D3×C13⋊C3, C22×C3⋊(C3⋊(D13⋊C3)), … |
| maximal normal subgroup of | C22×C32×D13⋊C3, C22×C3⋊D3×C13⋊C3, C22×C3⋊(C3⋊(D13⋊C3)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 217);