Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C59×#529 ⋊ C2 |
| Sylow | C59 ⋊ #3481 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D59 |
| commutator, socle | C22×C59 | C25 |
| Frattini | C22 | C24×D59 |
| Fitting | C59×#529 | C2 |
| hypercenter | #529 | D59 |
| hypocenter | C59 | #3481 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ #529 | |
1242 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|e^2=fg,b^a=bf,c^a=cg,d^b=df,h^c=h^58,h^d=h^58862 conjugacy classes — view the full character table.
| maximal subgroup of | #28555658, #28555664, #28555695, … |
| maximal normal subgroup of | #28555658, #28555664, #28555695, … |
| maximal quotient of | #28748133, #28748136, #28748138, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 18116);