Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C8 |
No aliases for this group.
| Sylow | C79 ⋊ #1450 |
212 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 212 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=d,b^2=e,d^2=f,e^2=g,h^a=h^78,c^b=cf1640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34178707, #34178709, #34178711, … |
| maximal normal subgroup of | #34178707, #34178709, #34178711, … |
| maximal quotient of | #34177626, #34177655, #34178699, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2794);