Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #2108 |
184 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 125 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=d,b^2=e,d^2=f,f^2=g,c^b=cg,h^b=h^782576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34175963, #34175965, #34175966, … |
| maximal normal subgroup of | #34175963, #34175965, #34175966, … |
| maximal quotient of | #34197250, #34197259, C16×#11929608, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6106);