Finite Group DatabasebetaFinite Group Databasebeta| order | 2752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C43 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D43 |
| commutator, socle | C2×C43 | C22×C8 |
| Fitting | #131×C43 | C2 |
| prime radical | #41×C43 | C4 |
| cosocle | C8×C43 | C23 |
| hypercenter | #131 | D43 |
| hypocenter | C43 | #504 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C8 ◁ #131 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1376 |
Polycyclic presentation:
2^6,43|a^2=d,d^2=e,e^2=f,g^a=g^42,c^b=cf460 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2752, 966);