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C2×C41×D35 #19153274

order5740
isoclinismisoclinic class of D35
automorphism?
homologyAbelianization (H1) = C22×C41 · Schur multiplier (H2) = C2

Aliases

direct productC2×C41×D35
unambiguous semidirect product(C2×C5)⋊(D7×C41)
unambiguous semidirect product(C2×C7)⋊(D5×C41)

Splittings

Fitting, socleC2×C5×C7×C41 ⋊ C2
derived, HallC5×C7 ⋊ C22×C41
HallC5×C7×C41 ⋊ C22
HallC7×C41 ⋊ C2×D5
HallC5×C41 ⋊ C2×D7
SylowC7 ⋊ C2×D5×C41
SylowC5 ⋊ C2×D7×C41

Subgroups

subgroupG/H
center, hypercenterC2×C41D35
commutator, hypocenterC5×C7C22×C41
FrattiniC1G
Fitting, socleC2×C5×C7×C41C2
LCSG ▷ C5×C7
UCSC1 ◁ C2×C41

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1558 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C41×C5⋊AGL(1,𝔽7), D3×C41×D35, C2×C41×D105, …
maximal normal subgroup ofC2×C41×C5⋊AGL(1,𝔽7), C2×C3×C41×D35, C2×D35×C41⋊C5, …
maximal quotient ofD3×C41×D35, C2×C41×D105, C2×C3×C41×D35, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5740, 41);