Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C59×#552 ⋊ C2 |
| Sylow | C59 ⋊ #3493 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D59 |
| commutator, socle | C22×C59 | C25 |
| Fitting | C59×#552 | C2 |
| hypercenter | #552 | D59 |
| hypocenter | C59 | #3493 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ #552 | |
1040 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|b^2=g,c^2=f,d^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^b=h^58,h^e=h^58769 conjugacy classes — view the full character table.
| maximal subgroup of | #29465945, #29465949, #29465968, … |
| maximal normal subgroup of | #29465945, #29465949, #29465968, … |
| maximal quotient of | #28748751, #28748976, #28748978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 18228);