Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #2821 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator, socle | C23×C59 | C24 |
| Fitting | C59×#397 | C2 |
| hypercenter | #397 | D59 |
| hypocenter | C59 | #2821 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #397 | |
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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=f,c^2=e,d^2=e,b^a=be,c^a=cf,c^b=cg,d^b=def,d^c=de,h^d=h^58664 conjugacy classes — view the full character table.
| maximal subgroup of | #28564246, #28564250, #28564268, … |
| maximal normal subgroup of | #28564246, #28564250, #28564268, … |
| maximal quotient of | #28519368, #28519382, #28519405, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 12567);