Finite Group DatabasebetaFinite Group Databasebeta| order | 1452 |
| isoclinism | isoclinic class of C3⋊#92150 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C3⋊#92150 |
| Fitting, socle, derived, Hall | C3×C112 ⋊ C4 |
| Sylow | C112 ⋊ Dic3 |
| Sylow | C3 ⋊ #92150 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C112 | C4 |
| prime radical, cosocle | C3×C11⋊D11 | C2 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 66 |
Polycyclic presentation:
2^2,3,11^2|a^2=b,c^a=c^2,d^a=d^8e^5,e^a=d^9e^3,d^b=d^10,e^b=e^1096 conjugacy classes — view the full character table.
| maximal subgroup of | #17983714, C9⋊#92150, C3⋊#13089721, … |
| maximal normal subgroup of | C3⋊(#92150⋊C3), C3×C3⋊#92150, C13×C3⋊#92150, … |
| maximal quotient of | C9⋊#92150, C3×C3⋊#92150, C3⋊(C3⋊#92150), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1452, 26);