Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C59 ⋊ #2986 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D59 |
| commutator, socle | C22×C59 | C23×C4 |
| Fitting | C59×#433 | C2 |
| hypercenter | #433 | D59 |
| hypocenter | C59 | #2986 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ #433 | |
330 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 161 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=f,b^2=e,c^2=e,f^2=g,b^a=be,d^a=de,c^b=ceg,d^b=dg,h^c=h^58862 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#2986, C2×#21433195, #29453668, … |
| maximal normal subgroup of | D59×#2986, C2×#21433195, #29453668, … |
| maximal quotient of | #28587446, #28587456, #28587457, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13609);