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C2×C7⋊(D41⋊C5) #19153251

order5740
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7⋊(D41⋊C5)
unambiguous semidirect product(C2×C7)⋊(D41⋊C5)
unambiguous semidirect product(C2×C41⋊C5)⋊D7
unambiguous semidirect product(C2×D287)⋊C5

Splittings

Fitting, socleC2×C7×C41 ⋊ C2×C5
derived, HallC7×C41 ⋊ C22×C5
HallC7×C41⋊C5 ⋊ C22
HallC2×D287 ⋊ C5
HallC41⋊C5 ⋊ C2×D7
SylowC41 ⋊ C2×C5×D7
SylowC7 ⋊ C2×D41⋊C5

Subgroups

subgroupG/H
center, hypercenterC2C7⋊(D41⋊C5)
commutator, hypocenterC7×C41C22×C5
FrattiniC1G
Fitting, socleC2×C7×C41C2×C5
LCSG ▷ C7×C41
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

106 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×ΓL(1,𝔽8)⋊(D41⋊C5), D3×C7⋊(D41⋊C5), C2×C3×C7⋊(D41⋊C5), …
maximal normal subgroup ofC2×ΓL(1,𝔽8)⋊(D41⋊C5), C2×C3×C7⋊(D41⋊C5), C2×C5×C7⋊(D41⋊C5)
maximal quotient ofD3×C7⋊(D41⋊C5), C2×C3×C7⋊(D41⋊C5), C2×C3⋊(C7⋊(D41⋊C5)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5740, 18);