Finite Group DatabasebetaFinite Group Databasebeta| order | 1952 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×#6923)⋊C4 |
| Fitting | C2×C4×C61 ⋊ C4 |
| Sylow | C61 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×#6923 |
| commutator | C2×C61 | C42 |
| Fitting | C2×C4×C61 | C4 |
| socle | C22×C61 | C2×C4 |
| prime radical, cosocle | C22×D61 | C22 |
| hypercenter | C2×C4 | #6923 |
| hypocenter | C61 | #95 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 488 |
Polycyclic presentation:
2^5,61|a^2=d,b^2=e,b^a=bc,f^a=f^11,f^d=f^60140 conjugacy classes — view the full character table.
| maximal subgroup of | #16840613, #16840614, #16840615, … |
| maximal normal subgroup of | #16840613, #16840614, #16840615, … |
| maximal quotient of | (C2×#6923)⋊C8, #16840628, #16840629, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1952, 197);