Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#117×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2498 |
546 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 153 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,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^781598 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34261851, #34261855, #34261866, … |
| maximal normal subgroup of | #34261851, #34261855, #34261866, … |
| maximal quotient of | #34210233, #34210974, #34211419, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 8948);