Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | #390×C79 ⋊ C2 |
| Sylow | C79 ⋊ C4×#127 |
924 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 237 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=e,c^2=f,d^2=g,b^a=be,c^a=cf,h^c=h^78,h^d=h^781148 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34176242, #34176323, #34176388, … |
| maximal normal subgroup of | #34176242, #34176323, #34176388, … |
| maximal quotient of | #34209452, #34209454, #390×Dic79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 7074);