Finite Group DatabasebetaFinite Group Databasebeta| order | 8428 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊Dic301 |
| unambiguous semidirect product | C43⋊(C7⋊Dic7) |
| derived, Hall | C72×C43 ⋊ C4 |
| Sylow | C72 ⋊ Dic43 |
| Sylow | C43 ⋊ C7⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊D301 |
| commutator, hypocenter | C72×C43 | C4 |
| Fitting, socle | C2×C72×C43 | C2 |
| LCS | G ▷ C72×C43 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2,7^2,43,2|a^2=e,b^a=b^6,c^a=c^6,d^a=d^422110 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #38760311, #38760312, #38760315, … |
| maximal normal subgroup of | #38760311, #38760312, #38760315, … |
| maximal quotient of | C3⋊(C7⋊Dic301), C3×C7⋊Dic301 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8428, 23);