Finite Group DatabasebetaFinite Group Databasebeta| order | 28420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C7⋊#10596817 |
| unambiguous semidirect product | C7⋊(C7×#10596817) |
| Fitting, socle, Hall | C5×C72×C29 ⋊ C4 |
| derived | C5×C7×C29 ⋊ C4×C7 |
| Hall | C72×C29 ⋊ Dic5 |
| Hall | C5×C72 ⋊ #1181 |
| Hall | C5×C29 ⋊ C7×Dic7 |
| Sylow | C72 ⋊ #10596817 |
| Sylow | C29 ⋊ C7×Dic35 |
| Sylow | C5 ⋊ C7×C7⋊#1181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C7⋊#10596817 |
| commutator, hypocenter | C5×C7×C29 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C29 | C4 |
| prime radical | C5×C72×D29 | C2 |
| cosocle | C5×C7×D29 | C2×C7 |
| LCS | G ▷ C5×C7×C29 | |
| UCS | C1 ◁ C7 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2030 |
1981 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28420, 131);