Finite Group DatabasebetaFinite Group Databasebeta| order | 10731 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C49×C73 ⋊ C3 |
| Sylow | C73 ⋊ C49⋊C3 |
| Sylow | C49 ⋊ C73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C49×C73 | C3 |
| Frattini | C7 | #13095276 |
| socle | C7×C73 | ΓL(1,𝔽8) |
| LCS | G ▷ C49×C73 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
3,7,73,7|b^7=d^4,b^a=b^4d,c^a=c^8,d^a=d^41195 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#24924355, #36339882, #36339886, … |
| maximal normal subgroup of | C2×#24924355, #36339882, #36339886, … |
| maximal quotient of | C2×#24924355, #44567124, C3×#24924355 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10731, 5);