Finite Group Databasebeta

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C3×C11×#63118⋊C3 #38788067

order25740
automorphism?
homologyAbelianization (H1) = C32×C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11×#63118⋊C3
unambiguous semidirect product#63118⋊(C32×C11)
unambiguous semidirect product(C3×#63118)⋊(C3×C11)
unambiguous semidirect product(C11×#63118)⋊C32
unambiguous semidirect product(C3×C11×#63118)⋊C3

Splittings

Fitting, socleC3×C5×C11×C13 ⋊ C3×C4
derived, HallC5×C13 ⋊ C32×C4×C11
HallC3×C5×C11×C13⋊C3 ⋊ C4
HallC11×#63118 ⋊ C32
HallC3×C11×C13⋊C3 ⋊ Dic5
HallC5×C11×C13 ⋊ C32×C4
HallC3×C5×C13⋊C3 ⋊ C4×C11
Hall#63118 ⋊ C32×C11
HallC11×C13 ⋊ C32×Dic5
HallC3×C13⋊C3 ⋊ C11×Dic5
HallC5×C11 ⋊ C3×AGL(1,𝔽13)
SylowC13 ⋊ C32×C11×Dic5
SylowC5 ⋊ C3×C11×AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC3×C11#63118⋊C3
commutator, hypocenterC5×C13C32×C4×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C13C3×C4
prime radicalC3×C5×C11×D13⋊C3C2
cosocleC5×D13C2×C32×C11
LCSG ▷ C5×C13
UCSC1 ◁ C3×C11

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2145

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 298);