Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C59×#533 ⋊ C2 |
| Sylow | C59 ⋊ #3444 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D59 |
| commutator, socle | C22×C59 | C25 |
| Frattini | C22 | C24×D59 |
| Fitting | C59×#533 | C2 |
| hypercenter | #533 | D59 |
| hypocenter | C59 | #3444 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ #533 | |
1212 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|d^2=g,e^2=f,b^a=bf,c^a=cg,h^a=h^58,h^c=h^58,h^d=h^58868 conjugacy classes — view the full character table.
| maximal subgroup of | #28555201, #28555224, #28555250, … |
| maximal normal subgroup of | #28555201, #28555224, #28555250, … |
| maximal quotient of | #28746990, #28747089, #28747094, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17807);