Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #488×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3212 |
400 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|b^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^78,c^b=ce,f^c=fg,h^d=h^78890 conjugacy classes — view the full character table.
| maximal subgroup of | #3212×D79, C2×#23774377, #35159501, … |
| maximal normal subgroup of | #3212×D79, C2×#23774377, #35159501, … |
| maximal quotient of | #34297596, #34297970, #34298818, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 15487);