Finite Group DatabasebetaFinite Group Databasebeta| order | 28420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C7 |
| direct product | C5×C7⋊(C7⋊#1181) |
| unambiguous semidirect product | C7⋊(C5×C7⋊#1181) |
| Fitting, socle, Hall | C5×C72×C29 ⋊ C4 |
| derived, Hall | C72×C29 ⋊ C4×C5 |
| Hall | C5×C72 ⋊ #1181 |
| Hall | C5×C29 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ C5×#1181 |
| Sylow | C29 ⋊ C5×C7⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C7⋊(C7⋊#1181) |
| commutator, hypocenter | C72×C29 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C29 | C4 |
| prime radical | C5×C72×D29 | C2 |
| cosocle | C72×D29 | C2×C5 |
| LCS | G ▷ C72×C29 | |
| UCS | C1 ◁ C5 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7105 |
1975 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28420, 108);