Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8⋊C8×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1623 |
228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|b^2=f,c^2=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^78,d^b=df,e^b=eg,h^b=h^78,d^c=dg,e^c=eg1118 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1623×D79, C2×#23762480, #34264166, … |
| maximal normal subgroup of | #1623×D79, C2×#23762480, #34264166, … |
| maximal quotient of | #34177011, #34177049, #34177050, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 3590);