Finite Group DatabasebetaFinite Group Databasebeta| order | 7648 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C239 ⋊ #103 |
42 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,239|a^2=d,b^2=e,c^2=e,b^a=bc,c^a=ce,c^b=ce,f^b=f^2381204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #103×D239, C2×#21439883, #29504765, … |
| maximal normal subgroup of | #103×D239, C2×#21439883, #29504765, … |
| maximal quotient of | #29504502, #29504508, #29504517, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7648, 69);