Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#436 ⋊ C2 |
| Sylow | C59 ⋊ #2976 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D59 |
| commutator, socle | C22×C59 | C23×C4 |
| Fitting | C59×#436 | C2 |
| hypercenter | #436 | D59 |
| hypocenter | C59 | #2976 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ #436 | |
412 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=f,f^2=g,b^a=be,d^a=de,c^b=ce,d^b=dg,h^c=h^58,h^d=h^58856 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#2976, C2×#21433140, #29453484, … |
| maximal normal subgroup of | D59×#2976, C2×#21433140, #29453484, … |
| maximal quotient of | #28587382, #28587404, #28587460, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13554);