Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C59×#340 ⋊ C2 |
| Sylow | C59 ⋊ #2035 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D59 |
| commutator | C22×C4×C59 | C23 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C59×#340 | C2 |
| socle | C23×C59 | C2×D4 |
| hypercenter | #340 | D59 |
| hypocenter | C59 | #2035 |
| LCS | G ▷ C22×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
316 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 85 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=g,c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^58,c^b=cf,h^b=h^58,e^c=eg,h^c=h^58844 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#2035, C2×#21425295, #28616165, … |
| maximal normal subgroup of | D59×#2035, C2×#21425295, #28616165, … |
| maximal quotient of | #28491988, #28492009, #28492078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 5709);