Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | C59⋊#1309 |
| Sylow | C59 ⋊ #1309 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C59⋊#95 |
| commutator | C23×C59 | C42 |
| Frattini | C2×C42 | C2×D59 |
| Fitting | C59×#423 | C2 |
| socle | C22×C59 | #95 |
| hypercenter | #423 | D59 |
| hypocenter | C59 | #1309 |
| LCS | G ▷ C23×C59 ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #423 | |
146 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bc,c^a=cf,e^a=eg,c^b=cg,d^b=df,h^b=h^58838 conjugacy classes — view the full character table.
| maximal subgroup of | #28476232, #28476233, #28476310, … |
| maximal normal subgroup of | #28476232, #28476233, #28476310, … |
| maximal quotient of | #28475264, #28475265, #28475285, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2423);