Finite Group DatabasebetaFinite Group Databasebeta| order | 1143 |
| isoclinism | isoclinic class of #11765919 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C127 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C127 | C9 |
| prime radical, cosocle | C127⋊C3 | C3 |
| LCS | G ▷ C127 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 127 |
| transitive degree | μt(G) = 127 |
Polycyclic presentation:
3^2,127|a^3=b,c^a=c^22,c^b=c^10723 conjugacy classes — view the full character table.
| maximal subgroup of | #11765919⋊C2, C2×#11765919, C3×#11765919, … |
| maximal normal subgroup of | #11765919⋊C2, C2×#11765919, C3×#11765919, … |
| maximal quotient of | C2×#11765919, #16812186, C3×#11765919, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1143, 3);