Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2396 |
528 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^78,c^b=cg,h^b=h^781604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34295755, #34295756, #34295766, … |
| maximal normal subgroup of | #34295755, #34295756, #34295766, … |
| maximal quotient of | #34209980, #34209982, #34209998, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 7786);