Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #2313 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator | C22×C59 | C23×C4 |
| Fitting | C59×#380 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | #380 | D59 |
| hypocenter | C59 | #2313 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #380 | |
512 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 189 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,b^2=f,c^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,h^b=h^58,h^c=h^58856 conjugacy classes — view the full character table.
| maximal subgroup of | #28482227, #28482673, #28482675, … |
| maximal normal subgroup of | #28482227, #28482673, #28482675, … |
| maximal quotient of | #28509934, #28509944, #28510006, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 7112);