Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | #385×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2379 |
520 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,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 | #2379×D79, C2×#23766573, #34450905, … |
| maximal normal subgroup of | #2379×D79, C2×#23766573, #34450905, … |
| maximal quotient of | #34209892, #34209899, #34209900, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 7683);