Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C59 ⋊ #2103 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #14273716 |
| commutator | C22×C4×C59 | C23 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C59×#424 | C2 |
| socle | C2×C59 | #400 |
| hypercenter | #424 | D59 |
| hypocenter | C59 | #2103 |
| LCS | G ▷ C22×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #424 | |
148 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,b^2=de,c^2=d,d^2=g,f^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,d^b=dg,e^b=eg,f^b=fg,h^b=h^58838 conjugacy classes — view the full character table.
| maximal subgroup of | #28502048, #28502050, #28502053, … |
| maximal normal subgroup of | #28502048, #28502050, #28502053, … |
| maximal quotient of | #28493814, #28493819, #28493824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6090);