Finite Group Databasebeta

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C3×C11×#11763979 #49114672

order36036
automorphism?
homologyAbelianization (H1) = C32×C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11×#11763979

Splittings

Fitting, socleC3×C7×C11×C13 ⋊ C3×C4
derived, HallC7×C13 ⋊ C32×C4×C11
HallC3×C7×C11×C13⋊C3 ⋊ C4
HallC11×C7⋊#261 ⋊ C32
HallC3×C11×C13⋊C3 ⋊ Dic7
HallC7×C11×C13 ⋊ C32×C4
HallC3×C7×C13⋊C3 ⋊ C4×C11
HallC7⋊#261 ⋊ C32×C11
HallC11×C13 ⋊ C32×Dic7
HallC3×C13⋊C3 ⋊ C11×Dic7
HallC7×C11 ⋊ C3×AGL(1,𝔽13)
SylowC13 ⋊ C32×C11×Dic7
SylowC7 ⋊ C3×C11×AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC3×C11#11763979
commutator, hypocenterC7×C13C32×C4×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C13C3×C4
prime radicalC3×C7×C11×D13⋊C3C2
cosocleC7×D13C2×C32×C11
LCSG ▷ C7×C13
UCSC1 ◁ C3×C11

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3003

Conjugacy classes & character table

1221 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 340);