Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C59×#342 ⋊ C2 |
| Sylow | C59 ⋊ C4×#99 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊C4×D59 |
| commutator | C22×C59 | C2×C42 |
| Frattini | C24 | C22×D59 |
| Fitting | C59×#342 | C2 |
| socle | C22×C59 | C2×C22⋊C4 |
| hypercenter | #342 | D59 |
| hypocenter | C59 | C4×#99 |
| LCS | G ▷ C22×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ #342 | |
412 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 107 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=e,b^2=f,c^2=e,b^a=bd,f^a=fg,d^b=dg,h^c=h^58682 conjugacy classes — view the full character table.
| maximal subgroup of | #28499010, #28499012, #28499015, … |
| maximal normal subgroup of | #28499010, #28499012, #28499015, … |
| maximal quotient of | #28479190, #28479194, #28479198, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4297);