Finite Group DatabasebetaFinite Group Databasebeta| order | 10647 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#16813063 |
| Fitting | C3×C7×C169 ⋊ C3 |
| derived, Hall | C7×C169 ⋊ C32 |
| Sylow | C169 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×C169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16813063 |
| commutator, cosocle, hypocenter | C7×C169 | C32 |
| Frattini | C13 | C3×#63270 |
| Fitting | C3×C7×C169 | C3 |
| socle | C3×C7×C13 | C13⋊C3 |
| LCS | G ▷ C7×C169 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
1191 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#20296858, C3×#20296862, C3×#20296864, … |
| maximal normal subgroup of | C3×#20296858, C3×#20296862, C3×#20296864, … |
| maximal quotient of | C2×C3×#16813063 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10647, 10);