Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#126×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2512 |
496 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=efg,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^78,h^c=h^78,h^d=h^781130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2512×D79, C2×#23767985, #34457415, … |
| maximal normal subgroup of | #2512×D79, C2×#23767985, #34457415, … |
| maximal quotient of | #34210291, #34210647, #34211445, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 9095);