Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2274 |
696 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=f,b^2=g,c^2=e,b^a=be,d^a=de,c^b=ce,h^d=h^781628 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34286066, #34286068, #34286070, … |
| maximal normal subgroup of | #34286066, #34286068, #34286070, … |
| maximal quotient of | #34209350, #34209353, #34209354, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6864);