Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C59 ⋊ C8×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D59 |
| commutator | C4×C59 | C22×C8 |
| Frattini | C42 | C22×D59 |
| Fitting | C59×Q8⋊C8 | C2 |
| socle | C22×C59 | C4×D4 |
| hypercenter | Q8⋊C8 | D59 |
| hypocenter | C59 | C8×Q16 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ Q8⋊C8 | |
164 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 73 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,b^2=f,c^2=ef,d^2=f,e^2=g,b^a=bd,d^a=df,d^b=df,h^c=h^58868 conjugacy classes — view the full character table.
| maximal subgroup of | C8×Q16×D59, C2×#21422900, #28558063, … |
| maximal normal subgroup of | C8×Q16×D59, C2×#21422900, #28558063, … |
| maximal quotient of | #28479459, #28479463, #28479917, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 3314);