Finite Group DatabasebetaFinite Group Databasebeta| order | 2752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C43 ⋊ #391 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D43 |
| commutator | C22×C43 | C22×C4 |
| Fitting | C22×Q8×C43 | C2 |
| socle, prime radical, cosocle | C23×C43 | C23 |
| hypercenter | C22×Q8 | D43 |
| hypocenter | C43 | #391 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2752 |
Polycyclic presentation:
2^6,43|a^2=f,b^2=def,c^2=e,b^a=bd,c^a=ce,g^a=g^42,g^b=g^42448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2752, 456);