Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M64×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1400 |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,d^b=dg,h^b=h^781604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1400×D79, C2×#23761539, #34208471, … |
| maximal normal subgroup of | #1400×D79, C2×#23761539, #34208471, … |
| maximal quotient of | #34175607, #34175667, #34175709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2649);