Finite Group Databasebeta

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C3×C5×C11×C49⋊C3 #37564677

order24255
automorphism?
homologyAbelianization (H1) = C32×C5×C11 · Schur multiplier (H2) = C3

Aliases

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

Splittings

FittingC3×C5×C11×C49 ⋊ C3
derived, SylowC49 ⋊ C32×C5×C11
HallC5×C11×C49 ⋊ C32
HallC11×C49 ⋊ C32×C5
HallC5×C49 ⋊ C32×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11C49⋊C3
commutator, cosocle, hypocenterC49C32×C5×C11
FrattiniC7C3×C5×C11×ΓL(1,𝔽8)
FittingC3×C5×C11×C49C3
socleC3×C5×C7×C11ΓL(1,𝔽8)
LCSG ▷ C49
UCSC1 ◁ C3×C5×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8085

Conjugacy classes & character table

3135 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24255, 8);