Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C59×D32 ⋊ C2 |
| Sylow | C59 ⋊ #2262 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D16×D59 |
| commutator | C16×C59 | C23 |
| Frattini | C16 | C22×D59 |
| Fitting | C59×D32 | C2 |
| socle | C2×C59 | C2×D16 |
| hypercenter | D32 | D59 |
| hypocenter | C59 | #2262 |
| LCS | G ▷ C16×C59 ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ D32 | |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|c^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,d^a=de,e^a=ef,f^a=fg,d^b=de,e^b=ef,f^b=fg,h^c=h^58589 conjugacy classes — view the full character table.
| maximal subgroup of | #28509740, #28509742, #28509745, … |
| maximal normal subgroup of | #28509740, #28509742, #28509745, … |
| maximal quotient of | #28509120, #28509189, D32×Dic59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6816);