Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C22⋊Q8×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2450 |
584 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=f,b^2=ef,c^2=f,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^781130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2450×D79, C2×#23767220, #34456036, … |
| maximal normal subgroup of | #2450×D79, C2×#23767220, #34456036, … |
| maximal quotient of | #34210277, #34210456, #34211125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 8330);