Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×#125×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D59 |
| commutator, socle | C22×C59 | C25 |
| Fitting | C2×#125×C59 | C2 |
| hypercenter | C2×#125 | D59 |
| hypocenter | C59 | #3504 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C2×#125 | |
988 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=g,c^2=fg,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^b=h^58856 conjugacy classes — view the full character table.
| maximal subgroup of | #28480953, #28556934, #28556938, … |
| maximal normal subgroup of | #28480953, #28556934, #28556938, … |
| maximal quotient of | #28748798, #28749143, #28749147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 18334);