Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C59×#455 ⋊ C2 |
| Sylow | C59 ⋊ #3288 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16838034 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#455 | C2 |
| socle | C2×C59 | D42 |
| hypercenter | #455 | D59 |
| hypocenter | C59 | #3288 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #455 | |
464 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^58,d^b=de,e^b=eg,h^b=h^58,f^c=fg,e^d=eg490 conjugacy classes — view the full character table.
| maximal subgroup of | #28509419, #28509423, #28509433, … |
| maximal normal subgroup of | #28509419, #28509423, #28509433, … |
| maximal quotient of | #28578040, #28578049, #28578099, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16279);