Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #388×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2337 |
540 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,b^2=eg,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,c^b=ce,h^b=h^78,h^c=h^781136 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2337×D79, C2×#23766211, #34447193, … |
| maximal normal subgroup of | #2337×D79, C2×#23766211, #34447193, … |
| maximal quotient of | #34209544, #34209600, #34209602, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 7321);