Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C79 ⋊ #1744 |
296 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 173 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=e,b^2=f,c^2=d,e^2=g,b^a=bd,h^b=h^782576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34175110, #34175112, C8×#14579071, … |
| maximal normal subgroup of | #34175110, #34175112, C8×#14579071, … |
| maximal quotient of | #34178692, #34178695, #34178696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4255);