Finite Group DatabasebetaFinite Group Databasebeta| order | 1953 |
| isoclinism | isoclinic class of #10620252 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C31 ⋊ C9 |
| Sylow | C31 ⋊ C7⋊C9 |
| Sylow | C7 ⋊ C31⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #10620252 |
| commutator, hypocenter | C7×C31 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C7×C31 | C3 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1953 |
Polycyclic presentation:
3^2,7,31|a^3=b,c^a=c^4,d^a=d^25225 conjugacy classes — view the full character table.
| maximal subgroup of | #16840856, #16840860, #16840862, … |
| maximal normal subgroup of | #16840856, #16840860, #16840862, … |
| maximal quotient of | C2×#14519869, #28331763, C7×#14519869, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1953, 3);