Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C79 ⋊ #3395 |
348 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 141 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,b^2=e,c^2=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^78,d^b=de,f^c=fg,h^c=h^781595 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34201789, #34201793, #34201817, … |
| maximal normal subgroup of | #34201789, #34201793, #34201817, … |
| maximal quotient of | #34305077, Q8×#14579095, #34308021, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 17516);