Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #1640 |
212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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=g,c^2=f,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^78,d^b=df,e^b=eg,d^c=dg,e^c=eg,h^c=h^78767 conjugacy classes — view the full character table.
| maximal subgroup of | #1640×D79, C2×#23762587, #34263953, … |
| maximal normal subgroup of | #1640×D79, C2×#23762587, #34263953, … |
| maximal quotient of | #34177183, #34177204, #34177267, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 3697);