Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #1942 |
248 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 107 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=f,c^2=eg,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^c=h^781136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1942×D79, C2×#23764130, #34291598, … |
| maximal normal subgroup of | #1942×D79, C2×#23764130, #34291598, … |
| maximal quotient of | #34186808, #34186828, #34186914, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5240);