Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C2×#117×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2500 |
568 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 153 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|a^2=eg,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^781598 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34185921, #34185923, #34197828, … |
| maximal normal subgroup of | #34185921, #34185923, #34197828, … |
| maximal quotient of | #34210241, #34210805, #34211443, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 8968);