Finite Group DatabasebetaFinite Group Databasebeta| order | 27468 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×AGL(1,𝔽7)×D109 |
| unambiguous semidirect product | D7⋊(C32×D109) |
| Fitting, socle | C3×C7×C109 ⋊ C22×C3 |
| derived, Hall | C7×C109 ⋊ C22×C32 |
| Hall | C3×ΓL(1,𝔽8)×C109 ⋊ C22 |
| Hall | D7×D109 ⋊ C32 |
| Sylow | C109 ⋊ C2×C3×AGL(1,𝔽7) |
| Hall | C3×ΓL(1,𝔽8) ⋊ C2×D109 |
| Sylow | C7 ⋊ C2×C32×D109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | AGL(1,𝔽7)×D109 |
| commutator, cosocle, hypocenter | C7×C109 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C109 | C22×C3 |
| LCS | G ▷ C7×C109 | |
| UCS | C1 ◁ C3 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2289 |
1176 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27468, 168);