Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C82×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1590 |
166 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 69 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,b^2=f,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^78,c^b=cg,d^b=df,h^b=h^782540 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1590×D79, C2×#23762292, #34258015, … |
| maximal normal subgroup of | #1590×D79, C2×#23762292, #34258015, … |
| maximal quotient of | #34179089, #34179096, #34179508, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 3402);