Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C59 ⋊ #2062 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14273695 |
| commutator | C24×C59 | C23 |
| Frattini | C24 | C22×D59 |
| Fitting | C59×#385 | C2 |
| socle | C22×C59 | #120 |
| hypercenter | #385 | D59 |
| hypocenter | C59 | #2062 |
| LCS | G ▷ C24×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ #385 | |
314 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|a^2=d,b^2=d,c^2=d,b^a=bd,c^a=ce,f^a=fg,c^b=cf,e^b=eg,h^b=h^58838 conjugacy classes — view the full character table.
| maximal subgroup of | #28501543, #28501545, #28501550, … |
| maximal normal subgroup of | #28501543, #28501545, #28501550, … |
| maximal quotient of | #28493090, #28493092, #28493095, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 5863);