Finite Group DatabasebetaFinite Group Databasebeta| order | 1952 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#6923 |
| commutator, socle | C2×C61 | C22×C4 |
| Fitting | Q8×C61 | C4 |
| prime radical | #11758226 | C2 |
| cosocle | Dic61 | C23 |
| hypercenter | Q8 | #6923 |
| hypocenter | C61 | #131 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 976 |
Polycyclic presentation:
2^5,61|a^2=d,d^2=e,f^a=f^11,c^b=ce,f^b=f^60,f^c=f^60,f^d=f^6095 conjugacy classes — view the full character table.
| maximal subgroup of | #16840805, #16840806, #16840807, … |
| maximal normal subgroup of | #16840805, #16840806, #16840807, … |
| maximal quotient of | #16840727, #16840737, #16840769, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1952, 234);