Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×C4⋊C4×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2486 |
624 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 173 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,d^2=e,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 | #34186040, #34186060, #34186225, … |
| maximal normal subgroup of | #34186040, #34186060, #34186225, … |
| maximal quotient of | #34210172, #34210500, #34211050, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 8812);