Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C79 ⋊ #2254 |
128 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=d,b^2=d,c^2=efg,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^782534 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34175928, #34175930, #34202233, … |
| maximal normal subgroup of | #34175928, #34175930, #34202233, … |
| maximal quotient of | #34204706, #34206304, #34206870, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6792);