Finite Group DatabasebetaFinite Group Databasebeta| order | 1952 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22×C4×C61 ⋊ C2 |
| Sylow | C61 ⋊ #123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D61 |
| commutator, socle, cosocle | C22×C61 | C23 |
| Fitting | C22×C4×C61 | C2 |
| prime radical | C2×C22⋊D61 | C2 |
| hypercenter | C22×C4 | D61 |
| hypocenter | C61 | #123 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C22×C4 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 976 |
Polycyclic presentation:
2^5,61|c^2=d,b^a=bd,c^a=ce,f^a=f^60494 conjugacy classes — view the full character table.
| maximal subgroup of | #16839951, #123×D61, C2×#14519760, … |
| maximal normal subgroup of | #16839951, #123×D61, C2×#14519760, … |
| maximal quotient of | #16839625, #16839635, #16839641, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1952, 129);