Finite Group Databasebeta

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C3×C11⋊C5×C49⋊C3 #37564675

order24255
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11⋊C5×C49⋊C3
unambiguous semidirect productC11⋊(C3×C5×C49⋊C3)
unambiguous semidirect product(C3×C11)⋊(C5×C49⋊C3)
unambiguous semidirect productC49⋊(C32×C11⋊C5)
unambiguous semidirect product(C3×C49)⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×C49⋊C3)⋊(C3×C5)
unambiguous semidirect product(C49×C11⋊C5)⋊C32
unambiguous semidirect product(C3×C11×C49⋊C3)⋊C5
unambiguous semidirect product(C3×C49×C11⋊C5)⋊C3

Splittings

FittingC3×C11×C49 ⋊ C3×C5
derived, HallC11×C49 ⋊ C32×C5
HallC3×C11×C49⋊C3 ⋊ C5
HallC49×C11⋊C5 ⋊ C32
SylowC49 ⋊ C32×C11⋊C5
SylowC11 ⋊ C3×C5×C49⋊C3

Subgroups

subgroupG/H
center, hypercenterC3C11⋊C5×C49⋊C3
commutator, cosocle, hypocenterC11×C49C32×C5
FrattiniC7C3×ΓL(1,𝔽8)×C11⋊C5
FittingC3×C11×C49C3×C5
socleC3×C7×C11C5×ΓL(1,𝔽8)
LCSG ▷ C11×C49
UCSC1 ◁ C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1617

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24255, 6);