Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×D8×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3168 |
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^78,h^c=h^781136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34198250, #34198255, #34198268, … |
| maximal normal subgroup of | #34198250, #34198255, #34198268, … |
| maximal quotient of | #34288814, #34292481, #34292489, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 15078);