Finite Group DatabasebetaFinite Group Databasebeta| order | 1952 |
| isoclinism | isoclinic class of D61 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C61 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D61 |
| commutator, hypocenter | C61 | C32 |
| Fitting, cosocle | C16×C61 | C2 |
| socle, prime radical | C2×C61 | C16 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C16 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 1952 |
Polycyclic presentation:
2^5,61|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^60512 conjugacy classes — view the full character table.
| maximal subgroup of | C32×D61, C2×#14519683, #16839595, … |
| maximal normal subgroup of | C32×D61, C2×#14519683, #16839595, … |
| maximal quotient of | #16839481, C2×#14519683 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1952, 52);