Finite Group Databasebeta

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C3×C11×C3⋊#66774 #46778088

order33660
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×C3⋊#66774
unambiguous semidirect productC3⋊(C3×C11×#66774)

Splittings

Fitting, socle, HallC32×C5×C11×C17 ⋊ C4
derivedC3×C5×C17 ⋊ C3×C4×C11
HallC32×C11×C17 ⋊ AGL(1,𝔽5)
HallC5×C11×C17 ⋊ C3×Dic3
HallC32×C5×C17 ⋊ C4×C11
HallC32×C5×C11 ⋊ Dic17
HallC11×C17 ⋊ C3×ΓL(1,𝔽16)
HallC32×C17 ⋊ C11×AGL(1,𝔽5)
HallC32×C11 ⋊ #66774
HallC5×C17 ⋊ C3×C11×Dic3
HallC5×C11 ⋊ C3×Dic51
HallC32×C5 ⋊ C11×Dic17
SylowC17 ⋊ C3×C11×ΓL(1,𝔽16)
SylowC32 ⋊ C11×#66774
SylowC5 ⋊ C3×C11×Dic51

Subgroups

subgroupG/H
center, hypercenterC3×C11C3⋊#66774
commutator, hypocenterC3×C5×C17C3×C4×C11
FrattiniC1G
Fitting, socleC32×C5×C11×C17C4
prime radicalC32×D5×C11×C17C2
cosocleC3×D5×C17C2×C3×C11
LCSG ▷ C3×C5×C17
UCSC1 ◁ C3×C11

112 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 5610

Conjugacy classes & character table

3465 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33660, 256);