Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | #379×C79 ⋊ C2 |
| Sylow | C79 ⋊ C4×#120 |
1224 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 249 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=g,d^2=g,b^a=be,c^a=cf,h^d=h^781148 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34197516, #34197714, #34294254, … |
| maximal normal subgroup of | #34197516, #34197714, #34294254, … |
| maximal quotient of | #34209413, #34209433, #379×Dic79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 7009);