Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #432×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2980 |
394 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 157 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=f,f^2=g,b^a=be,c^a=cg,d^a=de,c^b=ce,d^b=dg,h^b=h^78,d^c=dg,h^c=h^781130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34182670, #34182673, #34183215, … |
| maximal normal subgroup of | #34182670, #34182673, #34183215, … |
| maximal quotient of | #34286992, #34287032, #34287247, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 13580);