Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#126×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2823 |
456 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 133 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=ef,d^2=f,b^a=be,c^a=cf,c^b=cg,d^b=def,d^c=de,h^c=h^781118 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2823×D79, C2×#23771472, #34494814, … |
| maximal normal subgroup of | #2823×D79, C2×#23771472, #34494814, … |
| maximal quotient of | #34219024, #34219033, #34219035, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 12582);