Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #2096 |
254 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 89 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=dg,b^2=de,c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,c^b=cf,d^b=dg,e^b=eg,h^b=h^78,d^c=dg,e^c=eg1124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2096×D79, C2×#23764941, #34318065, … |
| maximal normal subgroup of | #2096×D79, C2×#23764941, #34318065, … |
| maximal quotient of | #34193260, #34193301, #34193326, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6051);