Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C79 ⋊ #2329 |
528 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,b^2=fg,c^2=f,b^a=be,c^a=cf,d^a=de,h^a=h^78,c^b=ce,h^b=h^781136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34182322, #34182326, #34182329, … |
| maximal normal subgroup of | #34182322, #34182326, #34182329, … |
| maximal quotient of | #34209524, #34209549, #34209644, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 7245);