Finite Group Databasebeta

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C11×C3⋊(#63118⋊C3) #38788091

order25740
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊(#63118⋊C3)
unambiguous semidirect productC3⋊(C11×#63118⋊C3)
unambiguous semidirect product(C3⋊#63118)⋊(C3×C11)
unambiguous semidirect product(C11×C3⋊#63118)⋊C3

Splittings

Fitting, socleC3×C5×C11×C13 ⋊ C3×C4
derivedC3×C5×C13 ⋊ C3×C4×C11
HallC3×C5×C11×C13⋊C3 ⋊ C4
HallC3×C11×C13⋊C3 ⋊ Dic5
HallC5×C11×C13 ⋊ C3×Dic3
HallC3×C5×C13⋊C3 ⋊ C4×C11
HallC11×C13 ⋊ C3×Dic15
HallC3×C13⋊C3 ⋊ C11×Dic5
HallC5×C13 ⋊ C3×C11×Dic3
HallC5×C11 ⋊ C3⋊AGL(1,𝔽13)
SylowC13 ⋊ C3×C11×Dic15
SylowC5 ⋊ C11×C3⋊AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(#63118⋊C3)
commutator, hypocenterC3×C5×C13C3×C4×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C13C3×C4
prime radicalC3×C5×C11×D13⋊C3C2
cosocleC3×C5×D13C2×C3×C11
LCSG ▷ C3×C5×C13
UCSC1 ◁ C11

112 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2145

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 322);