Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C59×#392 ⋊ C2 |
| Sylow | C59 ⋊ #2397 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator, socle | C23×C59 | C24 |
| Fitting | C59×#392 | C2 |
| hypercenter | #392 | D59 |
| hypocenter | C59 | #2397 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #392 | |
840 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 167 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=e,d^2=ef,b^a=be,c^a=cf,c^b=cg,h^d=h^58682 conjugacy classes — view the full character table.
| maximal subgroup of | #28499015, #28499452, #28561012, … |
| maximal normal subgroup of | #28499015, #28499452, #28561012, … |
| maximal quotient of | #28510422, #28510424, #28510469, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 7788);