Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C79 ⋊ #1407 |
98 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=d,b^2=g,c^2=f,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^78,c^b=cf,d^b=defg,e^b=eg,h^b=h^78,d^c=dfg,e^d=eg521 conjugacy classes — view the full character table.
| maximal subgroup of | #1407×D79, C2×#23761561, #34208554, … |
| maximal normal subgroup of | #1407×D79, C2×#23761561, #34208554, … |
| maximal quotient of | #34175649, #34175689, #34175780, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2671);