Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | Q8⋊C8×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1479 |
248 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 83 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=e,b^2=f,c^2=f,d^2=f,e^2=g,b^a=bd,d^a=df,c^b=cf,d^b=df,h^c=h^781136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1479×D79, C2×#23761793, #34254640, … |
| maximal normal subgroup of | #1479×D79, C2×#23761793, #34254640, … |
| maximal quotient of | #34176256, #34176265, #34176293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2903);