Finite Group DatabasebetaFinite Group Databasebeta| order | 1404 |
| isoclinism | isoclinic class of (C3⋊(D13⋊C3))⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊(D13⋊C3))⋊D3 |
| unambiguous semidirect product | ((C3⋊D3)⋊D13)⋊C3 |
| Fitting, socle, derived | C32×C13 ⋊ C22×C3 |
| Hall | C32×C13⋊C3 ⋊ C22 |
| Sylow | C13 ⋊ C3×D32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C13 | C22×C3 |
| LCS | G ▷ C32×C13 | |
| UCS | C1 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 78 |
Polycyclic presentation:
2^2,3^3,13|d^a=d^2,f^a=f^12,d^b=d^2,e^b=e^2,f^c=f^339 conjugacy classes — view the full character table.
| maximal subgroup of | D32×D13⋊C3, C2×(C3⋊(D13⋊C3))⋊D3, #72242074, … |
| maximal normal subgroup of | D32×D13⋊C3, C2×(C3⋊(D13⋊C3))⋊D3 |
| maximal quotient of | #72241939, C2×(C3⋊(D13⋊C3))⋊D3, #72241982, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1404, 188);