Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2392 |
696 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^b=h^78,h^c=h^781604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34183367, #34183372, #34260540, … |
| maximal normal subgroup of | #34183367, #34183372, #34260540, … |
| maximal quotient of | #34209949, #34209968, #34210008, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 7750);