Finite Group Databasebeta

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C2×C5⋊(C11⋊(D49⋊C3)) #44568372

order32340
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊(C11⋊(D49⋊C3))
unambiguous semidirect product(C2×C5)⋊(C11⋊(D49⋊C3))
unambiguous semidirect product(C2×C11)⋊(C5⋊(D49⋊C3))
unambiguous semidirect product(C2×C49⋊C3)⋊D55
unambiguous semidirect product(C2×D2695)⋊C3

Splittings

FittingC2×C5×C11×C49 ⋊ C2×C3
derived, HallC5×C11×C49 ⋊ C22×C3
HallC2×D2695 ⋊ C3
HallC5×C11×C49⋊C3 ⋊ C22
HallC11×C49⋊C3 ⋊ C2×D5
HallC5×C49⋊C3 ⋊ C2×D11
HallC11×C49 ⋊ C2×C3×D5
HallC5×C49 ⋊ C2×C3×D11
HallC49⋊C3 ⋊ C2×D55
HallC5×C11 ⋊ C2×D49⋊C3
SylowC49 ⋊ C2×C3×D55
SylowC11 ⋊ C2×C5⋊(D49⋊C3)
SylowC5 ⋊ C2×C11⋊(D49⋊C3)

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(C11⋊(D49⋊C3))
commutator, cosocle, hypocenterC5×C11×C49C22×C3
FrattiniC7C2×C5⋊(C11⋊AGL(1,𝔽7))
FittingC2×C5×C11×C49C2×C3
socleC2×C5×C7×C11AGL(1,𝔽7)
LCSG ▷ C5×C11×C49
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5390

Conjugacy classes & character table

1054 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 74);