Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×M16×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2971 |
402 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=dg,c^b=cg,h^b=h^78,d^c=dg1610 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34184070, #34184074, #34184084, … |
| maximal normal subgroup of | #34184070, #34184074, #34184084, … |
| maximal quotient of | #34286556, #34286558, #34286707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 13528);