Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #427×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3348 |
348 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=eg,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,h^b=h^78,f^c=fg1121 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3348×D79, C2×#23775911, #35166927, … |
| maximal normal subgroup of | #3348×D79, C2×#23775911, #35166927, … |
| maximal quotient of | #34304568, #34304628, #34305983, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 17021);