Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C59 ⋊ #2101 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D59 |
| commutator | C22×C4×C59 | C23 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C59×#340 | C2 |
| socle | C23×C59 | C2×D4 |
| hypercenter | #340 | D59 |
| hypocenter | C59 | #2101 |
| LCS | G ▷ C22×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
198 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 79 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=dg,b^2=de,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^58,c^b=cf,f^b=fg,h^b=h^58,f^c=fg,h^c=h^58844 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#2101, C2×#21425669, #28618604, … |
| maximal normal subgroup of | D59×#2101, C2×#21425669, #28618604, … |
| maximal quotient of | #28493829, #28496603, #28496954, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6083);