Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C79 ⋊ #2950 |
456 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 181 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=f,b^2=g,c^2=fg,e^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,h^b=h^78,d^c=dg,h^c=h^781136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34204391, #34204395, #34204900, … |
| maximal normal subgroup of | #34204391, #34204395, #34204900, … |
| maximal quotient of | #34257742, #34257966, #34258113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 13377);