Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C59 ⋊ #2748 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator, socle | C23×C59 | C24 |
| Fitting | C59×#386 | C2 |
| hypercenter | #386 | D59 |
| hypocenter | C59 | #2748 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #386 | |
464 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 137 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=efg,b^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^b=h^58,h^d=h^58844 conjugacy classes — view the full character table.
| maximal subgroup of | #28507822, #28507823, #28508362, … |
| maximal normal subgroup of | #28507822, #28507823, #28508362, … |
| maximal quotient of | #28516145, #28516613, #28517260, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 11721);