Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C59×#553 ⋊ C2 |
| Sylow | C59 ⋊ #3512 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D59 |
| commutator, socle | C22×C59 | C25 |
| Fitting | C59×#553 | C2 |
| hypercenter | #553 | D59 |
| hypocenter | C59 | #3512 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ #553 | |
1032 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|b^2=g,c^2=fg,d^2=f,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^c=h^58,h^e=h^58769 conjugacy classes — view the full character table.
| maximal subgroup of | #29466667, #29466669, #29466671, … |
| maximal normal subgroup of | #29466667, #29466669, #29466671, … |
| maximal quotient of | #28748842, #28749070, #28749162, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 18428);