Finite Group Databasebeta

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C11×C3⋊#11758266 #44568857

order32340
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C7

Aliases

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

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C4
derived, HallC3×C5×C72 ⋊ C4×C11
HallC5×C72×C11 ⋊ Dic3
HallC3×C72×C11 ⋊ AGL(1,𝔽5)
HallC72×C11 ⋊ ΓL(1,𝔽16)
HallC5×C72 ⋊ C11×Dic3
HallC3×C5×C11 ⋊ #5997
HallC3×C72 ⋊ C11×AGL(1,𝔽5)
HallC5×C11 ⋊ C3⋊#5997
SylowC72 ⋊ C11×ΓL(1,𝔽16)
HallC3×C11 ⋊ #11758266
HallC3×C5 ⋊ C11×#5997
SylowC5 ⋊ C11×C3⋊#5997
SylowC3 ⋊ C11×#11758266

Subgroups

subgroupG/H
center, hypercenterC11C3⋊#11758266
commutator, hypocenterC3×C5×C72C4×C11
FrattiniC1G
Fitting, socleC3×C5×C72×C11C4
prime radicalC3×C11×C5⋊(C7⋊D7)C2
cosocleC3×C5⋊(C7⋊D7)C2×C11
LCSG ▷ C3×C5×C72
UCSC1 ◁ C11

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

2079 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 559);