Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #1746 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D59 |
| commutator | C22×C59 | C2×C42 |
| Fitting | C2×C4×C8×C59 | C2 |
| socle | C23×C59 | C22×C4 |
| hypercenter | C2×C4×C8 | D59 |
| hypocenter | C59 | #1746 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×C8 | |
240 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=e,b^2=f,c^2=d,e^2=g,b^a=bd,c^b=cg,h^b=h^581912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475534, #28475536, #28479144, … |
| maximal normal subgroup of | #28475534, #28475536, #28479144, … |
| maximal quotient of | #28479115, #28479118, #28479121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4261);