Finite Group Databasebeta

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C3×C11⋊#11758266 #44568810

order32340
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C7

Aliases

direct productC3×C11⋊#11758266
unambiguous semidirect productC11⋊(C3×#11758266)

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C4
derived, HallC5×C72×C11 ⋊ C3×C4
HallC3×C72×C11 ⋊ AGL(1,𝔽5)
HallC3×C5×C72 ⋊ Dic11
HallC72×C11 ⋊ C3×AGL(1,𝔽5)
HallC5×C72 ⋊ C3×Dic11
HallC3×C5×C11 ⋊ #5997
HallC3×C72 ⋊ C11⋊AGL(1,𝔽5)
HallC5×C11 ⋊ C3×#5997
SylowC72 ⋊ C3×C11⋊AGL(1,𝔽5)
HallC3×C11 ⋊ #11758266
HallC3×C5 ⋊ C11⋊#5997
SylowC11 ⋊ C3×#11758266
SylowC5 ⋊ C3×C11⋊#5997

Subgroups

subgroupG/H
center, hypercenterC3C11⋊#11758266
commutator, hypocenterC5×C72×C11C3×C4
FrattiniC1G
Fitting, socleC3×C5×C72×C11C4
prime radicalC3×C11×C5⋊(C7⋊D7)C2
cosocleC11×C5⋊(C7⋊D7)C2×C3
LCSG ▷ C5×C72×C11
UCSC1 ◁ C3

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

2055 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 512);