Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#123×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2422 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator, socle | C23×C59 | C24 |
| Fitting | C2×#123×C59 | C2 |
| hypercenter | C2×#123 | D59 |
| hypocenter | C59 | #2422 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×#123 | |
652 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|b^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^58,h^d=h^58850 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#2422, C2×#21427607, #28756606, … |
| maximal normal subgroup of | D59×#2422, C2×#21427607, #28756606, … |
| maximal quotient of | #28510637, #28511021, #28511491, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 8021);