Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #383×C79 ⋊ C2 |
| Sylow | C79 ⋊ C4×#126 |
516 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 189 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,b^2=ef,c^2=e,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 | C4×#126×D79, C2×#23765948, #34446763, … |
| maximal normal subgroup of | C4×#126×D79, C2×#23765948, #34446763, … |
| maximal quotient of | #34209422, #34209441, #383×Dic79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 7058);