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 ⋊ #3120 |
372 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,b^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^78,d^b=dg,h^b=h^78,f^c=fg,h^c=h^781124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3120×D79, C2×#23773620, #35156632, … |
| maximal normal subgroup of | #3120×D79, C2×#23773620, #35156632, … |
| maximal quotient of | #34288385, #34291351, #34291371, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 14730);