Finite Group DatabasebetaFinite Group Databasebeta| order | 8428 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| direct product | D43×C7⋊D7 |
| unambiguous semidirect product | (C7×D43)⋊D7 |
| Fitting, socle, derived, Hall | C72×C43 ⋊ C22 |
| Sylow | C72 ⋊ C2×D43 |
| Sylow | C43 ⋊ C2×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C43 | C22 |
| LCS | G ▷ C72×C43 | |
| UCS | C1 | |
100 conjugacy classes of subgroups.
598 conjugacy classes — view the full character table.
| maximal subgroup of | #14268588⋊D7, #14268587⋊D7, D43×ΓL(1,𝔽8)⋊D7, … |
| maximal normal subgroup of | #14268588⋊D7, #14268587⋊D7, D43×ΓL(1,𝔽8)⋊D7, … |
| maximal quotient of | C3×D43×C7⋊D7, D43×C3⋊(C7⋊D7), C7⋊D7×D129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8428, 31);