Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C22⋊Q8×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2681 |
618 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=f,b^2=e,c^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^78,c^b=cg,d^b=de,h^c=h^78,h^d=h^781124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34495213, #34495218, #34495239, … |
| maximal normal subgroup of | #34495213, #34495218, #34495239, … |
| maximal quotient of | #34215593, #34215601, #34215620, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 10865);