Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C59 ⋊ #1289 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C59⋊#95 |
| commutator | C2×C4×C59 | C42 |
| Frattini | C23×C4 | C2×D59 |
| Fitting | C59×#380 | C2 |
| socle | C22×C59 | #95 |
| hypercenter | #380 | D59 |
| hypocenter | C59 | #1289 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ #380 | |
228 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 77 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=d,b^2=e,c^2=fg,e^2=fg,b^a=bc,c^a=cf,e^a=efg,d^b=dg,h^b=h^58844 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1289, C2×#21421963, #28478562, … |
| maximal normal subgroup of | D59×#1289, C2×#21421963, #28478562, … |
| maximal quotient of | #28475226, #28475237, #28475239, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2377);