Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #1916 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D59 |
| commutator | C22×C59 | C22×C8 |
| Fitting | C59×#336 | C2 |
| socle | C23×C59 | C22×C4 |
| hypercenter | #336 | D59 |
| hypocenter | C59 | #1916 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ #336 | |
240 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 105 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=f,b^2=f,c^2=d,f^2=g,b^a=bd,c^a=ce,h^b=h^58,h^c=h^581216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#1916, C2×#21424652, #28590743, … |
| maximal normal subgroup of | D59×#1916, C2×#21424652, #28590743, … |
| maximal quotient of | #28486805, #28486812, #28486819, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 5066);