Finite Group DatabasebetaFinite Group Databasebeta| order | 1952 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#92420 |
| Sylow | C61 ⋊ C22⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×#6923 |
| commutator | C2×C61 | C2×C8 |
| Fitting, prime radical | C23×C61 | C4 |
| socle | C22×C61 | C2×C4 |
| cosocle | C2×Dic61 | C22 |
| hypercenter | C23 | #6923 |
| hypocenter | C61 | C22⋊C8 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C23 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 976 |
Polycyclic presentation:
2^5,61|a^2=d,d^2=e,b^a=bc,f^a=f^11,f^d=f^60140 conjugacy classes — view the full character table.
| maximal subgroup of | #16840605, #16840606, #16840607, … |
| maximal normal subgroup of | #16840605, #16840606, #16840607, … |
| maximal quotient of | #16840605, #16840607, D4⋊#92420, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1952, 202);