Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#435 ⋊ C2 |
| Sylow | C59 ⋊ #3321 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D236 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#435 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #435 | D59 |
| hypocenter | C59 | #3321 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ #435 | |
392 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=eg,b^2=g,c^2=g,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^58,c^b=cg,d^b=de,f^c=fg,h^c=h^58841 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3321, C2×#21436284, #29465457, … |
| maximal normal subgroup of | D59×#3321, C2×#21436284, #29465457, … |
| maximal quotient of | #28604276, #28604994, #28605778, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16698);