Finite Group Databasebeta

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C7×C11×#3866⋊C3 #46803178

order34188
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C11 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC7×C11×C37 ⋊ C3×C4
derived, SylowC37 ⋊ C3×C4×C7×C11
HallC7×C11×#3866 ⋊ C3
HallC7×C11×C37⋊C3 ⋊ C4
HallC11×#3866 ⋊ C3×C7
HallC11×C37⋊C3 ⋊ C4×C7
HallC7×#3866 ⋊ C3×C11
HallC7×C37⋊C3 ⋊ C4×C11
HallC11×C37 ⋊ C3×C4×C7
HallC7×C37 ⋊ C3×C4×C11
Hall#3866 ⋊ C3×C7×C11
HallC37⋊C3 ⋊ C4×C7×C11

Subgroups

subgroupG/H
center, hypercenterC7×C11#3866⋊C3
commutator, hypocenterC37C3×C4×C7×C11
FrattiniC1G
Fitting, socleC7×C11×C37C3×C4
prime radicalC7×C11×D37⋊C3C2
cosocleD37C2×C3×C7×C11
LCSG ▷ C37
UCSC1 ◁ C7×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2849

Conjugacy classes & character table

1155 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 50);