Finite Group Databasebeta

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C3×C11×C3⋊#63121 #38788192

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

Aliases

direct productC3×C11×C3⋊#63121
unambiguous semidirect productC3⋊(C3×C11×#63121)

Splittings

Fitting, socle, HallC32×C5×C11×C13 ⋊ C4
derivedC3×C5×C13 ⋊ C3×C4×C11
HallC32×C11×C13 ⋊ AGL(1,𝔽5)
HallC5×C11×C13 ⋊ C3×Dic3
HallC32×C5×C13 ⋊ C4×C11
HallC32×C5×C11 ⋊ #261
HallC11×C13 ⋊ C3×ΓL(1,𝔽16)
HallC32×C13 ⋊ C11×AGL(1,𝔽5)
HallC32×C11 ⋊ #63121
HallC5×C13 ⋊ C3×C11×Dic3
HallC5×C11 ⋊ C3×C3⋊#261
HallC32×C5 ⋊ C11×#261
SylowC13 ⋊ C3×C11×ΓL(1,𝔽16)
SylowC32 ⋊ C11×#63121
SylowC5 ⋊ C3×C11×C3⋊#261

Subgroups

subgroupG/H
center, hypercenterC3×C11C3⋊#63121
commutator, hypocenterC3×C5×C13C3×C4×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C13C4
prime radicalC32×C11×D65C2
cosocleC3×D65C2×C3×C11
LCSG ▷ C3×C5×C13
UCSC1 ◁ C3×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) = 4290

Conjugacy classes & character table

1782 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 423);