Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×Q32×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2189 |
220 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|a^2=g,c^2=g,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,d^b=df,f^b=fg,h^b=h^78,h^c=h^78887 conjugacy classes — view the full character table.
| maximal subgroup of | #2189×D79, C2×#23765339, #34442043, … |
| maximal normal subgroup of | #2189×D79, C2×#23765339, #34442043, … |
| maximal quotient of | #34200393, #34200737, #34201497, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6449);