Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | D4×Q8×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3554 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D59 |
| commutator, socle | C22×C59 | C25 |
| Fitting | D4×Q8×C59 | C2 |
| hypercenter | D4×Q8 | D59 |
| hypocenter | C59 | #3554 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1022 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|b^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,h^a=h^58,c^b=cg,d^b=df,h^d=h^58763 conjugacy classes — view the full character table.
| maximal subgroup of | #28566748, #28566756, #28566763, … |
| maximal normal subgroup of | #28566748, #28566756, #28566763, … |
| maximal quotient of | #28751589, #28751715, #28751859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 18982);