Finite Group DatabasebetaFinite Group Databasebeta| order | 1952 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C61 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×#6923 |
| commutator, socle | C2×C61 | C2×C8 |
| Fitting | C8×C61 | C4 |
| prime radical | C2×D61 | C8 |
| cosocle | #92418 | C22 |
| hypercenter | C8 | #6923 |
| hypocenter | C61 | M32 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C4 ◁ C8 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 976 |
Polycyclic presentation:
2^5,61|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^11,f^b=f^60,f^c=f^60140 conjugacy classes — view the full character table.
| maximal subgroup of | #16840652, #16840653, #16840678, … |
| maximal normal subgroup of | #16840652, #16840653, #16840678, … |
| maximal quotient of | #16840651, #16840657, #16840683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1952, 221);