Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C4×C8×C59 ⋊ C2 |
| Sylow | C59 ⋊ #1476 |
276 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|a^2=e,c^2=f,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^58,d^b=df,h^b=h^581912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28479360, #28479362, #28479365, … |
| maximal normal subgroup of | #28479360, #28479362, #28479365, … |
| maximal quotient of | #28476629, #28476637, #28476639, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2893);