Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×M16×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2875 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D59 |
| commutator | C2×C59 | C22×C42 |
| Fitting | C4×M16×C59 | C2 |
| socle | C22×C59 | C23×C4 |
| hypercenter | C4×M16 | D59 |
| hypocenter | C59 | #2875 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C4×M16 | |
556 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=e,b^2=f,e^2=g,b^a=bg,h^a=h^58,d^c=dg,h^d=h^581228 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28485499, #28485503, #28485506, … |
| maximal normal subgroup of | #28485499, #28485503, #28485506, … |
| maximal quotient of | #28554283, #28554304, #28554363, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 12939);