Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×SD16×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3376 |
346 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,b^2=e,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,h^b=h^78,f^c=fg1121 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3376×D79, C2×#23776223, #35168081, … |
| maximal normal subgroup of | #3376×D79, C2×#23776223, #35168081, … |
| maximal quotient of | #34304936, #34305136, #34307264, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 17333);