Finite Group DatabasebetaFinite Group Databasebeta| order | 1952 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8×C61 ⋊ C4 |
| Sylow | C61 ⋊ #97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×#6923 |
| commutator, socle | C2×C61 | C42 |
| Fitting | C8×C61 | C4 |
| prime radical | C2×D61 | C2×C4 |
| cosocle | C4×D61 | C22 |
| hypercenter | C8 | #6923 |
| hypocenter | C61 | #97 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C4 ◁ C8 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 488 |
Polycyclic presentation:
2^5,61|a^2=c,b^2=d,c^2=e,b^a=be,f^b=f^11,f^d=f^60140 conjugacy classes — view the full character table.
| maximal subgroup of | #16840652, #16840653, C2×#14519831, … |
| maximal normal subgroup of | #16840652, #16840653, C2×#14519831, … |
| maximal quotient of | #16840603, #92420⋊C8, (C2×#6923)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1952, 200);