Finite Group Databasebeta

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C11⋊C5×C22⋊(C49⋊C3) #44568349

order32340
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC11⋊C5×C22⋊(C49⋊C3)
unambiguous semidirect productC22⋊(C11⋊C5×C49⋊C3)
unambiguous semidirect productC11⋊(C5×C22⋊(C49⋊C3))
unambiguous semidirect productC49⋊(A4×C11⋊C5)
unambiguous semidirect product(C22×C11⋊C5)⋊(C49⋊C3)
unambiguous semidirect product(C49×C11⋊C5)⋊A4
unambiguous semidirect product(C11×C22⋊(C49⋊C3))⋊C5

Splittings

Fitting, derived, HallC22×C11×C49 ⋊ C3×C5
HallC22×C49×C11⋊C5 ⋊ C3
HallC11×C22⋊(C49⋊C3) ⋊ C5
HallC49×C11⋊C5 ⋊ A4
HallC11×C49 ⋊ C5×A4
HallC22×C11⋊C5 ⋊ C49⋊C3
HallC22×C49 ⋊ C3×C11⋊C5
SylowC49 ⋊ A4×C11⋊C5
HallC22×C11 ⋊ C5×C49⋊C3
SylowC11 ⋊ C5×C22⋊(C49⋊C3)
SylowC22 ⋊ C11⋊C5×C49⋊C3

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC22×C11×C49C3×C5
FrattiniC7C11⋊C5×C22⋊ΓL(1,𝔽8)
socleC22×C7×C11C5×ΓL(1,𝔽8)
LCSG ▷ C22×C11×C49
UCSC1

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2156

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 51);