Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C59×#386 ⋊ C2 |
| Sylow | C59 ⋊ #2325 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator | C22×C59 | C23×C4 |
| Fitting | C59×#386 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | #386 | D59 |
| hypocenter | C59 | #2325 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #386 | |
696 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=g,b^2=g,c^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,h^b=h^58,h^c=h^58,h^d=h^58856 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#2325, C2×#21426798, #28747495, … |
| maximal normal subgroup of | D59×#2325, C2×#21426798, #28747495, … |
| maximal quotient of | #28509942, #28509983, #28509987, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 7212);