Finite Group DatabasebetaFinite Group Databasebeta| order | 21294 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#20296858 |
| Fitting | C3×C7×C169 ⋊ C2×C3 |
| derived, Hall | C7×C169 ⋊ C2×C32 |
| Hall | C3×#16813063 ⋊ C2 |
| Hall | C7×D169 ⋊ C32 |
| Hall | D169 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C169 ⋊ C2×C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×D169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #20296858 |
| commutator, cosocle, hypocenter | C7×C169 | C2×C32 |
| Frattini | C13 | C3×#10587716 |
| Fitting | C3×C7×C169 | C2×C3 |
| socle | C3×C7×C13 | D13⋊C3 |
| LCS | G ▷ C7×C169 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3549 |
618 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21294, 35);