Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #327×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1519 |
340 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 71 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=e,c^2=g,d^2=g,b^a=bd,c^a=cg,d^a=df,c^b=cf,d^b=dg,e^b=efg,h^c=h^78773 conjugacy classes — view the full character table.
| maximal subgroup of | #1519×D79, C2×#23761966, #34255593, … |
| maximal normal subgroup of | #1519×D79, C2×#23761966, #34255593, … |
| maximal quotient of | #34176252, #34176256, #34176318, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 3076);