Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C59 ⋊ #2374 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator | C22×C59 | C23×C4 |
| Fitting | C59×#386 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | #386 | D59 |
| hypocenter | C59 | #2374 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #386 | |
552 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 185 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=g,c^2=ef,d^2=ef,b^a=be,c^a=cf,d^b=de,h^b=h^58,h^c=h^58,h^d=h^58862 conjugacy classes — view the full character table.
| maximal subgroup of | #28505446, #28505450, #28505953, … |
| maximal normal subgroup of | #28505446, #28505450, #28505953, … |
| maximal quotient of | #28510153, #28510243, #28510278, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 7643);