Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C59×#424 ⋊ C2 |
| Sylow | C59 ⋊ #2053 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14273716 |
| commutator | C22×C4×C59 | C23 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C59×#424 | C2 |
| socle | C2×C59 | #394 |
| hypercenter | #424 | D59 |
| hypocenter | C59 | #2053 |
| LCS | G ▷ C22×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #424 | |
264 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|c^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^58,c^b=cf,d^b=dg,f^b=fg,h^b=h^58838 conjugacy classes — view the full character table.
| maximal subgroup of | #28501198, #28501200, #28501203, … |
| maximal normal subgroup of | #28501198, #28501200, #28501203, … |
| maximal quotient of | #28492425, #28492432, #28492439, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 5816);