Finite Group Databasebeta

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C11×C3⋊(C7⋊#3866) #46803269

order34188
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C3⋊(C7⋊#3866)
unambiguous semidirect productC3⋊(C11×C7⋊#3866)
unambiguous semidirect productC7⋊(C11×C3⋊#3866)

Splittings

Fitting, socle, HallC3×C7×C11×C37 ⋊ C4
derived, HallC3×C7×C37 ⋊ C4×C11
HallC7×C11×C37 ⋊ Dic3
HallC3×C11×C37 ⋊ Dic7
HallC11×C37 ⋊ Dic21
HallC7×C37 ⋊ C11×Dic3
HallC3×C7×C11 ⋊ #3866
HallC3×C37 ⋊ C11×Dic7
HallC7×C11 ⋊ C3⋊#3866
SylowC37 ⋊ C11×Dic21
HallC3×C11 ⋊ C7⋊#3866
HallC3×C7 ⋊ C11×#3866
SylowC7 ⋊ C11×C3⋊#3866
SylowC3 ⋊ C11×C7⋊#3866

Subgroups

subgroupG/H
center, hypercenterC11C3⋊(C7⋊#3866)
commutator, hypocenterC3×C7×C37C4×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C37C4
prime radicalC3×C7×C11×D37C2
cosocleC3×C7×D37C2×C11
LCSG ▷ C3×C7×C37
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8547

Conjugacy classes & character table

2343 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 141);