Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×D8×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3008 |
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|e^2=g,b^a=be,c^a=cf,e^a=eg,e^b=eg,d^c=dg,h^c=h^781124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34319789, #34319791, #34325651, … |
| maximal normal subgroup of | #34319789, #34319791, #34325651, … |
| maximal quotient of | #34261425, #34261513, #34261601, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 13774);