Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C59 ⋊ #3028 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#14273696 |
| commutator | C23×C59 | C24 |
| Frattini | C23 | C23×D59 |
| Fitting | C59×#585 | C2 |
| socle | C2×C59 | C2×#120 |
| hypercenter | #585 | D59 |
| hypocenter | C59 | #3028 |
| LCS | G ▷ C23×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #585 | |
716 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 161 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=g,d^2=g,b^a=be,c^a=cf,d^a=dg,h^a=h^58,f^b=fg,e^c=eg1015 conjugacy classes — view the full character table.
| maximal subgroup of | #28507679, #28507680, #28507683, … |
| maximal normal subgroup of | #28507679, #28507680, #28507683, … |
| maximal quotient of | #28562728, #28562735, #28562742, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13916);