Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C59 ⋊ #3230 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D236 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#431 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #431 | D59 |
| hypocenter | C59 | #3230 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #431 | |
360 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 141 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=g,b^2=e,c^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^58,c^b=ce,f^c=fg,h^c=h^581192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28485212, #28485214, #28485338, … |
| maximal normal subgroup of | #28485212, #28485214, #28485338, … |
| maximal quotient of | #28598178, #28598369, #28599211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 15663);