Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C4×D4×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3519 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D59 |
| commutator, socle | C22×C59 | C25 |
| Fitting | C2×C4×D4×C59 | C2 |
| hypercenter | C2×C4×D4 | D59 |
| hypocenter | C59 | #3519 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C2×C4×D4 | |
1252 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|e^2=fg,b^a=bf,c^a=cg,e^a=ef,h^a=h^58,d^b=df1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28480569, #28480573, #28555883, … |
| maximal normal subgroup of | #28480569, #28480573, #28555883, … |
| maximal quotient of | #28748905, #28749409, #28749451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 18542);