Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C59 ⋊ C8×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D59 |
| commutator | C2×C59 | C2×C4×C8 |
| Fitting | C2×C22⋊C8×C59 | C2 |
| socle | C23×C59 | C22×C4 |
| hypercenter | C2×C22⋊C8 | D59 |
| hypocenter | C59 | C8×C22⋊C4 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C22⋊C8 | |
384 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 165 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=e,e^2=g,b^a=bd,h^a=h^58,h^b=h^58,h^c=h^581240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28479229, #28479233, #28479241, … |
| maximal normal subgroup of | #28479229, #28479233, #28479241, … |
| maximal quotient of | C22⋊C8×C59⋊C8, #28479165, #28479182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4284);