Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Fitting | C2×C4⋊Q8×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2858 |
752 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 197 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=g,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=dg,h^a=h^78,h^b=h^78,h^d=h^781136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34187318, #34187328, #34187333, … |
| maximal normal subgroup of | #34187318, #34187328, #34187333, … |
| maximal quotient of | #34219460, #34219538, #34219611, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 12868);