Finite Group Databasebeta

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C11×#11758266⋊C3 #44568647

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#11758266⋊C3
unambiguous semidirect product#11758266⋊(C3×C11)
unambiguous semidirect product(C11×#11758266)⋊C3

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C3×C4
derived, HallC5×C72 ⋊ C3×C4×C11
HallC11×#11758266 ⋊ C3
HallC5×C11×#3861 ⋊ C4
HallC11×#3861 ⋊ AGL(1,𝔽5)
Hall#11758266 ⋊ C3×C11
HallC5×#3861 ⋊ C4×C11
HallC72×C11 ⋊ C3×AGL(1,𝔽5)
Hall#3861 ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ #5997⋊C3
SylowC72 ⋊ C3×C11×AGL(1,𝔽5)
SylowC5 ⋊ C11×#5997⋊C3

Subgroups

subgroupG/H
center, hypercenterC11#11758266⋊C3
commutator, hypocenterC5×C72C3×C4×C11
FrattiniC1G
Fitting, socleC5×C72×C11C3×C4
prime radicalC11×C5⋊#64424C2
cosocleC5⋊(C7⋊D7)C2×C3×C11
LCSG ▷ C5×C72
UCSC1 ◁ C11

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 770

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 349);