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C2×C7×D43⋊C7 #22554593

order8428
automorphism?
homologyAbelianization (H1) = C22×C72 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C7×D43⋊C7
unambiguous semidirect productD43⋊(C2×C72)
unambiguous semidirect product(C2×D43)⋊C72
unambiguous semidirect product(C43⋊C7)⋊(C22×C7)
unambiguous semidirect product(C2×C43⋊C7)⋊(C2×C7)
unambiguous semidirect product(C2×C7×D43)⋊C7

Splittings

Fitting, socleC2×C7×C43 ⋊ C2×C7
derived, SylowC43 ⋊ C22×C72
HallC7×C43⋊C7 ⋊ C22
HallC2×D43 ⋊ C72

Subgroups

subgroupG/H
center, hypercenterC2×C7D43⋊C7
commutator, hypocenterC43C22×C72
FrattiniC1G
Fitting, socleC2×C7×C43C2×C7
LCSG ▷ C43
UCSC1 ◁ C2×C7

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

238 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C7×AGL(1,𝔽43), C2×#14268588⋊C7, C2×#14268587⋊C7, …
maximal normal subgroup ofC2×C7×AGL(1,𝔽43), C2×#14268588⋊C7, C2×#14268587⋊C7, …
maximal quotient ofD3×C7×D43⋊C7, C2×C3×C7×D43⋊C7, C2×C7×C3⋊(D43⋊C7)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8428, 26);