Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C8 |
No aliases for this group.
| Sylow | C79 ⋊ #1709 |
212 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|b^2=dg,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^b=h^78,h^c=h^78896 conjugacy classes — view the full character table.
| maximal subgroup of | #34176128, #34201666, #34201672, … |
| maximal normal subgroup of | #34176128, #34201666, #34201672, … |
| maximal quotient of | #34182045, #34188024, #34188033, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4115);