Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C22×C4 |
| unambiguous semidirect product | C59⋊#1273 |
| Sylow | C59 ⋊ #1273 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C42 | C2×D59 |
| commutator | C2×C59 | C82 |
| Fitting | C2×C4×C8×C59 | C2 |
| socle | C23×C59 | C42 |
| hypercenter | C2×C4×C8 | D59 |
| hypocenter | C59 | #1273 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C42 ◁ C2×C4×C8 | |
212 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,b^2=e,d^2=f,e^2=g,b^a=bc,h^b=h^581936 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475461, #28475462, #28475474, … |
| maximal normal subgroup of | #28475461, #28475462, #28475474, … |
| maximal quotient of | C59⋊#7014, #28475216, #28475217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2337);