Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C59 ⋊ #2032 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16837314 |
| commutator | C24×C59 | C23 |
| Frattini | C24 | C22×D59 |
| Fitting | C2×#99×C59 | C2 |
| socle | C2×C59 | #393 |
| hypercenter | C2×#99 | D59 |
| hypocenter | C59 | #2032 |
| LCS | G ▷ C24×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2 ◁ C24 ◁ C2×#99 | |
278 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 278 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|a^2=d,b^2=d,b^a=bd,c^a=ce,e^a=eg,f^a=fg,c^b=cf,f^b=fg,h^b=h^58,d^c=dg661 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#2032, C2×#21425273, #28616129, … |
| maximal normal subgroup of | D59×#2032, C2×#21425273, #28616129, … |
| maximal quotient of | #28491835, #28491837, #28491839, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 5687);