Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C59×#346 ⋊ C2 |
| Sylow | C59 ⋊ C4×M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D59 |
| commutator | C2×C59 | C2×C4×C8 |
| Fitting | C59×#346 | C2 |
| socle | C22×C59 | C22×C8 |
| hypercenter | #346 | D59 |
| hypocenter | C59 | C4×M32 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C8 ◁ #346 | |
196 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 113 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=d,b^2=e,d^2=f,f^2=g,c^a=cg,h^b=h^58,h^c=h^581240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28497688, #28497692, #28497696, … |
| maximal normal subgroup of | #28497688, #28497692, #28497696, … |
| maximal quotient of | #28497667, #28497681, #28497714, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6103);