Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C8 |
No aliases for this group.
| Sylow | C59 ⋊ #1709 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14273723 |
| commutator | C42×C59 | C23 |
| Frattini | C42 | C22×D59 |
| Fitting | C59×#493 | C2 |
| socle | C22×C59 | #127 |
| hypercenter | #493 | D59 |
| hypocenter | C59 | #1709 |
| LCS | G ▷ C42×C59 ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #493 | |
212 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|b^2=dg,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^b=h^58,h^c=h^58676 conjugacy classes — view the full character table.
| maximal subgroup of | #28476548, #28502086, #28502092, … |
| maximal normal subgroup of | #28476548, #28502086, #28502092, … |
| maximal quotient of | #28482465, #28488444, #28488453, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4115);