Finite Group Databasebeta

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C7×C3⋊(C11⋊#3866) #46803263

order34188
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC3×C7×C11×C37 ⋊ C4
derived, HallC3×C11×C37 ⋊ C4×C7
HallC7×C11×C37 ⋊ Dic3
HallC3×C7×C37 ⋊ Dic11
HallC11×C37 ⋊ C7×Dic3
HallC7×C37 ⋊ Dic33
HallC3×C7×C11 ⋊ #3866
HallC3×C37 ⋊ C7×Dic11
HallC7×C11 ⋊ C3⋊#3866
SylowC37 ⋊ C7×Dic33
HallC3×C11 ⋊ C7×#3866
HallC3×C7 ⋊ C11⋊#3866
SylowC11 ⋊ C7×C3⋊#3866
SylowC3 ⋊ C7×C11⋊#3866

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(C11⋊#3866)
commutator, hypocenterC3×C11×C37C4×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C37C4
prime radicalC3×C7×C11×D37C2
cosocleC3×C11×D37C2×C7
LCSG ▷ C3×C11×C37
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8547

Conjugacy classes & character table

2331 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 135);