Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C59 ⋊ #1985 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D59 |
| commutator, socle | C23×C59 | C22×C4 |
| Fitting | C2×C4×Q8×C59 | C2 |
| hypercenter | C2×C4×Q8 | D59 |
| hypocenter | C59 | #1985 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×Q8 | |
280 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 121 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=def,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^58,c^b=cg,h^b=h^581204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475904, #28475909, #28476004, … |
| maximal normal subgroup of | #28475904, #28475909, #28476004, … |
| maximal quotient of | #28488685, #28488689, #28488693, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 5451);