Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #1377 |
140 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bc,c^a=cg,h^a=h^78,d^b=dg1604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34175018, #34175019, #34175030, … |
| maximal normal subgroup of | #34175018, #34175019, #34175030, … |
| maximal quotient of | #34175103, #34175113, #34175120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2594);