Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #340×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1736 |
448 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=e,b^2=f,d^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=cg,h^c=h^781136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1736×D79, C2×#23763118, #34285675, … |
| maximal normal subgroup of | #1736×D79, C2×#23763118, #34285675, … |
| maximal quotient of | #34177729, #34177739, #34177751, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 4228);