Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Sylow | C59 ⋊ #2858 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator, socle | C23×C59 | C24 |
| Fitting | C2×#127×C59 | C2 |
| hypercenter | C2×#127 | D59 |
| hypocenter | C59 | #2858 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
752 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|b^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=dg,h^b=h^58,h^d=h^58856 conjugacy classes — view the full character table.
| maximal subgroup of | #28487740, #28487750, #28487755, … |
| maximal normal subgroup of | #28487740, #28487750, #28487755, … |
| maximal quotient of | #28519880, #28519962, #28520029, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 12866);