Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2649 |
434 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=eg,d^2=f,b^a=be,c^a=cf,c^b=cg,d^c=de,h^c=h^781592 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2649×D79, C2×#23769397, #34454797, … |
| maximal normal subgroup of | #2649×D79, C2×#23769397, #34454797, … |
| maximal quotient of | #34214723, #34214753, #34214836, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 10507);