Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C4⋊Q8×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2658 |
612 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 165 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=ef,b^2=eg,d^2=e,b^a=be,c^a=cf,c^b=cg,h^b=h^78,d^c=de,h^c=h^781124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34189650, #34189654, #34189706, … |
| maximal normal subgroup of | #34189650, #34189654, #34189706, … |
| maximal quotient of | #34214797, #34214799, #34214802, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 10622);