Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #1713 |
192 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=f,b^2=df,c^2=eg,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^782534 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34175001, #34175003, #34175004, … |
| maximal normal subgroup of | #34175001, #34175003, #34175004, … |
| maximal quotient of | #34182050, #34188028, #34188036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4128);