Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C4×#41×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3483 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D59 |
| commutator, socle | C22×C59 | C25 |
| Frattini | C22 | C24×D59 |
| Fitting | C4×#41×C59 | C2 |
| hypercenter | C4×#41 | D59 |
| hypocenter | C59 | #3483 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C4×#41 | |
1202 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|b^2=f,c^2=f,d^2=f,e^2=fg,b^a=bf,c^a=cg,d^b=df,h^c=h^581210 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28480742, #28480743, #28555684, … |
| maximal normal subgroup of | #28480742, #28480743, #28555684, … |
| maximal quotient of | #28748168, #28748172, #28748173, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 18136);