Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#478 ⋊ C2 |
| Sylow | C59 ⋊ #3240 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D59 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#478 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #478 | D59 |
| hypocenter | C59 | #3240 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #478 | |
328 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|b^2=eg,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,h^b=h^58,f^c=fg,h^d=h^58577 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3240, C2×#21435335, #29460856, … |
| maximal normal subgroup of | D59×#3240, C2×#21435335, #29460856, … |
| maximal quotient of | #28598230, #28598433, #28599267, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 15749);