Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C59 ⋊ #1726 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D59 |
| commutator | C2×C59 | C43 |
| Fitting | C59×#376 | C2 |
| socle | C23×C59 | C22×C4 |
| hypercenter | #376 | D59 |
| hypocenter | C59 | #1726 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ #376 | |
328 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,b^2=e,c^2=f,d^2=g,h^a=h^58,c^b=cg1240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28479127, #28479131, #28479135, … |
| maximal normal subgroup of | #28479127, #28479131, #28479135, … |
| maximal quotient of | #28478043, #28478046, #28478052, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4197);