Finite Group Databasebeta

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C3×C11×C3⋊(C7⋊#261) #49114908

order36036
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×C3⋊(C7⋊#261)
unambiguous semidirect productC3⋊(C3×C11×C7⋊#261)

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C4
derivedC3×C7×C13 ⋊ C3×C4×C11
HallC32×C11×C13 ⋊ Dic7
HallC7×C11×C13 ⋊ C3×Dic3
HallC32×C7×C13 ⋊ C4×C11
HallC32×C7×C11 ⋊ #261
HallC11×C13 ⋊ C3×Dic21
HallC32×C13 ⋊ C11×Dic7
HallC32×C11 ⋊ C7⋊#261
HallC7×C13 ⋊ C3×C11×Dic3
HallC7×C11 ⋊ C3×C3⋊#261
HallC32×C7 ⋊ C11×#261
SylowC13 ⋊ C3×C11×Dic21
SylowC32 ⋊ C11×C7⋊#261
SylowC7 ⋊ C3×C11×C3⋊#261

Subgroups

subgroupG/H
center, hypercenterC3×C11C3⋊(C7⋊#261)
commutator, hypocenterC3×C7×C13C3×C4×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C13C4
prime radicalC32×C7×C11×D13C2
cosocleC3×C7×D13C2×C3×C11
LCSG ▷ C3×C7×C13
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) = 6006

Conjugacy classes & character table

2871 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 576);