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C2×C32×D41⋊C5 #20301602

order7380
isoclinismisoclinic class of D41⋊C5
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×D41⋊C5
unambiguous semidirect productD41⋊(C2×C32×C5)
unambiguous semidirect product(C2×D41)⋊(C32×C5)
unambiguous semidirect product(C41⋊C5)⋊(C22×C32)
unambiguous semidirect product(C2×C41⋊C5)⋊(C2×C32)
unambiguous semidirect product(C2×C3×D41)⋊(C3×C5)
unambiguous semidirect product(C2×C32×D41)⋊C5

Splittings

Fitting, socleC2×C32×C41 ⋊ C2×C5
derived, SylowC41 ⋊ C22×C32×C5
HallC32×C41⋊C5 ⋊ C22
HallC2×C32×D41 ⋊ C5
HallC32×C41 ⋊ C22×C5
HallC41⋊C5 ⋊ C22×C32
HallC2×D41 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C32D41⋊C5
commutator, hypocenterC41C22×C32×C5
FrattiniC1G
Fitting, socleC2×C32×C41C2×C5
LCSG ▷ C41
UCSC1 ◁ C2×C32

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×D5×D41⋊C5, C2×C32×C5×D41⋊C5, C2×C32×C5⋊(D41⋊C5)
maximal normal subgroup ofC2×C32×C5×D41⋊C5
maximal quotient ofC2×C32×D41⋊C25, C32×D5×D41⋊C5, C2×C32×C5×D41⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7380, 80);