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C32×C7⋊(D41⋊C5) #38788943

order25830
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×C7⋊(D41⋊C5)
unambiguous semidirect product(C41⋊C5)⋊(C32×D7)
unambiguous semidirect product(C32×D287)⋊C5

Splittings

Fitting, socle, HallC32×C7×C41 ⋊ C2×C5
derived, HallC7×C41 ⋊ C2×C32×C5
HallC32×C7×C41⋊C5 ⋊ C2
HallC32×D287 ⋊ C5
HallC32×C41⋊C5 ⋊ D7
HallC7×C41⋊C5 ⋊ C2×C32
HallD287 ⋊ C32×C5
HallC32×C41 ⋊ C5×D7
HallC41⋊C5 ⋊ C32×D7
HallC32×C7 ⋊ D41⋊C5
SylowC41 ⋊ C32×C5×D7
SylowC7 ⋊ C32×D41⋊C5

Subgroups

subgroupG/H
center, hypercenterC32C7⋊(D41⋊C5)
commutator, cosocle, hypocenterC7×C41C2×C32×C5
FrattiniC1G
Fitting, socleC32×C7×C41C2×C5
LCSG ▷ C7×C41
UCSC1 ◁ C32

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2583

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 47);