Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #364×C79 ⋊ C2 |
| Sylow | C79 ⋊ #1357 |
112 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=d,c^2=f,d^2=ef,e^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,c^b=cf,d^b=defg,e^b=eg,h^b=h^781115 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1357×D79, C2×#23761436, #34199478, … |
| maximal normal subgroup of | #1357×D79, C2×#23761436, #34199478, … |
| maximal quotient of | #34174989, #34174999, #34175004, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2546);