Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C59×#585 ⋊ C2 |
| Sylow | C59 ⋊ #3584 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×C22⋊D59 |
| commutator | C4×C59 | C25 |
| Frattini | C4 | C24×D59 |
| Fitting | C59×#585 | C2 |
| socle | C2×C59 | C23×D4 |
| hypercenter | #585 | D59 |
| hypocenter | C59 | #3584 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C4 ◁ C2×#41 ◁ #585 | |
1424 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|e^2=g,f^2=g,b^a=bf,f^a=fg,f^b=fg,h^b=h^58,d^c=dg1030 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28604642, #28604645, #28604653, … |
| maximal normal subgroup of | #28604642, #28604645, #28604653, … |
| maximal quotient of | #29452252, #29452254, #29452365, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 19281);