Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C59 ⋊ #2799 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator, socle | C23×C59 | C24 |
| Fitting | C59×#400 | C2 |
| hypercenter | #400 | D59 |
| hypocenter | C59 | #2799 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #400 | |
376 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 129 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=eg,b^2=e,c^2=fg,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^58,c^b=cg,d^b=de,h^b=h^58,h^c=h^58,h^d=h^58670 conjugacy classes — view the full character table.
| maximal subgroup of | #28500932, #28500936, #28501518, … |
| maximal normal subgroup of | #28500932, #28500936, #28501518, … |
| maximal quotient of | #28516977, #28517375, #28517401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 12398);