Finite Group DatabasebetaFinite Group Databasebeta| order | 1053 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C33 |
| direct product | C32×C13⋊C9 |
| derived, Sylow | C13 ⋊ C32×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33 | C13⋊C3 |
| commutator, hypocenter | C13 | C32×C9 |
| Frattini | C3 | C32×C13⋊C3 |
| Fitting, socle, prime radical | C33×C13 | C3 |
| cosocle | C3×C13 | C33 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C33 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1053 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C13⋊#6855, #15691487, #15691489, … |
| maximal normal subgroup of | C13⋊#6855, #15691487, #15691489, … |
| maximal quotient of | C3×C9×C13⋊C9, C3×C32⋊(C13⋊C9), C3×#11760427, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1053, 39);