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C2×C7⋊(D43⋊C7) #22554594

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

Aliases

direct productC2×C7⋊(D43⋊C7)
unambiguous semidirect product(C2×C7)⋊(D43⋊C7)
unambiguous semidirect product(C2×C43⋊C7)⋊D7
unambiguous semidirect product(C2×D301)⋊C7

Splittings

Fitting, socleC2×C7×C43 ⋊ C2×C7
derivedC7×C43 ⋊ C22×C7
HallC7×C43⋊C7 ⋊ C22
SylowC43 ⋊ C2×C7×D7

Subgroups

subgroupG/H
center, hypercenterC2C7⋊(D43⋊C7)
commutator, hypocenterC7×C43C22×C7
FrattiniC1G
Fitting, socleC2×C7×C43C2×C7
LCSG ▷ C7×C43
UCSC1 ◁ C2

52 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#14268594⋊C7, C2×#14268593⋊C7, C2×ΓL(1,𝔽8)⋊(D43⋊C7), …
maximal normal subgroup ofC2×#14268594⋊C7, C2×#14268593⋊C7, C2×ΓL(1,𝔽8)⋊(D43⋊C7), …
maximal quotient ofD3×C7⋊(D43⋊C7), C2×C3×C7⋊(D43⋊C7), C2×C3⋊(C7⋊(D43⋊C7))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8428, 27);