Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #1384 |
132 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=d,b^2=e,c^2=f,e^2=fg,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,h^a=h^78,d^b=dg1592 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34175836, #34175837, #34175839, … |
| maximal normal subgroup of | #34175836, #34175837, #34175839, … |
| maximal quotient of | #34175145, #34175193, #34175309, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2612);