Finite Group DatabasebetaFinite Group Databasebeta| order | 28420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C7 |
| direct product | C29×C7⋊(C7⋊AGL(1,𝔽5)) |
| unambiguous semidirect product | C7⋊(C29×C7⋊AGL(1,𝔽5)) |
| Fitting, socle, Hall | C5×C72×C29 ⋊ C4 |
| derived, Hall | C5×C72 ⋊ C4×C29 |
| Hall | C72×C29 ⋊ AGL(1,𝔽5) |
| Hall | C5×C29 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ AGL(1,𝔽5)×C29 |
| Sylow | C5 ⋊ C29×C7⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | C7⋊(C7⋊AGL(1,𝔽5)) |
| commutator, hypocenter | C5×C72 | C4×C29 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C29 | C4 |
| prime radical | C72×D5×C29 | C2 |
| cosocle | C72×D5 | C2×C29 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C29 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7105 |
2929 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28420, 122);