Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C4⋊C8×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1923 |
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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=f,b^2=df,c^2=d,f^2=g,b^a=bd,c^a=ce,h^b=h^78,h^c=h^781616 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1923×D79, C2×#23764005, #34290557, … |
| maximal normal subgroup of | #1923×D79, C2×#23764005, #34290557, … |
| maximal quotient of | #34186441, #34186448, #34186455, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5115);