Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3352 |
336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 113 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=eg,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^78,c^b=cg,d^b=de,h^b=h^78,f^c=fg,h^d=h^781121 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34201923, #34201927, #34201937, … |
| maximal normal subgroup of | #34201923, #34201927, #34201937, … |
| maximal quotient of | #34304682, #34306040, #34306495, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 17086);