Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#490 ⋊ C2 |
| Sylow | C59 ⋊ #3368 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D59 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#490 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #490 | D59 |
| hypocenter | C59 | #3368 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #490 | |
382 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|b^2=e,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^c=h^58,h^d=h^58493 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3368, C2×#21436822, #29468496, … |
| maximal normal subgroup of | D59×#3368, C2×#21436822, #29468496, … |
| maximal quotient of | #28605333, #28605522, #28607650, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17236);