Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C59 ⋊ #1311 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4×C8 | C2×D59 |
| commutator | C2×C59 | C82 |
| Fitting | C82×C59 | C2 |
| socle | C22×C59 | C4×C8 |
| hypercenter | C82 | D59 |
| hypocenter | C59 | #1311 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C4×C8 ◁ C82 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=bg,h^a=h^581936 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475306, #28475355, #28475356, … |
| maximal normal subgroup of | #28475306, #28475355, #28475356, … |
| maximal quotient of | #28475304, #28475517, #28476019, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2427);