Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C79 ⋊ #3388 |
334 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=e,b^2=e,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^78,c^b=cg,d^b=de,h^b=h^78,f^c=fg770 conjugacy classes — view the full character table.
| maximal subgroup of | #3388×D79, C2×#23776349, #35168832, … |
| maximal normal subgroup of | #3388×D79, C2×#23776349, #35168832, … |
| maximal quotient of | #34304944, #34304953, #34306579, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 17459);