Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #2276 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator | C2×C59 | C22×C42 |
| Fitting | C59×#376 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | #376 | D59 |
| hypocenter | C59 | #2276 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #376 | |
628 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 325 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=g,c^2=ef,d^2=e,b^a=be,d^a=de,c^b=ce,h^d=h^581228 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28485588, #28485592, #28485602, … |
| maximal normal subgroup of | #28485588, #28485592, #28485602, … |
| maximal quotient of | #28509773, #28509775, #28509977, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6873);