Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×D8×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3179 |
374 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^78,c^b=cg,d^b=dg,h^b=h^781124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3179×D79, C2×#23774087, #35158163, … |
| maximal normal subgroup of | #3179×D79, C2×#23774087, #35158163, … |
| maximal quotient of | #34288852, #34292567, #34292571, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 15197);