Finite Group DatabasebetaFinite Group Databasebeta| order | 1524 |
| isoclinism | isoclinic class of D127⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C127⋊C3)⋊C4 |
| unambiguous semidirect product | Dic127⋊C3 |
| derived, Sylow | C127 ⋊ C3×C4 |
| Hall | Dic127 ⋊ C3 |
| Hall | C127⋊C3 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D127⋊C3 |
| commutator, hypocenter | C127 | C3×C4 |
| Fitting, socle, cosocle | C2×C127 | C2×C3 |
| prime radical | C2×C127⋊C3 | C2 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 131 |
| transitive degree | μt(G) = 508 |
Polycyclic presentation:
2,3,2,127|a^2=c,d^a=d^126,d^b=d^1954 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1524, 1);