Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C59 ⋊ #1370 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | D236 |
| commutator | C4×C59 | C2×C16 |
| Frattini | C4×C8 | C2×D59 |
| Fitting | C82×C59 | C2 |
| socle | C22×C59 | C4⋊C8 |
| hypercenter | C82 | D59 |
| hypocenter | C59 | #1370 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C8 ◁ C4×C8 ◁ C82 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,b^2=ce,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^581912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475338, #28475339, #28475341, … |
| maximal normal subgroup of | #28475338, #28475339, #28475341, … |
| maximal quotient of | #28475429, #28475431, #28475552, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2580);