Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #2216 |
154 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 57 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=g,b^2=df,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^782534 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34175826, #34175828, #34175832, … |
| maximal normal subgroup of | #34175826, #34175828, #34175832, … |
| maximal quotient of | #34202480, #34202531, #34202599, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6601);