Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2334 |
476 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,b^2=g,c^2=e,d^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,h^c=h^781604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2334×D79, C2×#23766169, #34447191, … |
| maximal normal subgroup of | #2334×D79, C2×#23766169, #34447191, … |
| maximal quotient of | #34209541, #34209595, #34209598, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 7279);