Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #1378 |
132 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 73 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,b^a=bc,e^a=eg,h^a=h^78,c^b=cg,h^b=h^781604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1378×D79, C2×#23761487, #34203293, … |
| maximal normal subgroup of | #1378×D79, C2×#23761487, #34203293, … |
| maximal quotient of | #34175106, #34175116, #34175123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2597);