Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#440 ⋊ C2 |
| Sylow | C59 ⋊ #3403 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D59 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#440 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #440 | D59 |
| hypocenter | C59 | #3403 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #440 | |
380 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|b^2=e,c^2=eg,d^2=eg,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^d=h^58667 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3403, C2×#21437185, #29469733, … |
| maximal normal subgroup of | D59×#3403, C2×#21437185, #29469733, … |
| maximal quotient of | #28605576, #28605580, #28607576, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17599);