Finite Group Databasebeta

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C3×C11⋊#11763982 #49114666

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

Aliases

direct productC3×C11⋊#11763982
unambiguous semidirect productC11⋊(C3×#11763982)

Splittings

Fitting, socleC3×C7×C11×C13 ⋊ C3×C4
derived, HallC7×C11×C13 ⋊ C32×C4
HallC3×C11×#63270 ⋊ C4
HallC7×C11⋊#261 ⋊ C32
HallC3×#63270 ⋊ Dic11
HallC11⋊#261 ⋊ C3×ΓL(1,𝔽8)
HallC11×C13 ⋊ C3×C4×ΓL(1,𝔽8)
HallC7×C13 ⋊ C32×Dic11
HallC7×C11 ⋊ C3×AGL(1,𝔽13)
SylowC13 ⋊ C3×ΓL(1,𝔽8)×Dic11
SylowC11 ⋊ C3×#11763982
SylowC7 ⋊ C3×C11⋊AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC3C11⋊#11763982
commutator, hypocenterC7×C11×C13C32×C4
FrattiniC1G
Fitting, socleC3×C7×C11×C13C3×C4
prime radicalC3×C11×#10587716C2
cosocleC7×C11×D13C2×C32
LCSG ▷ C7×C11×C13
UCSC1 ◁ C3

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3003

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 334);