Finite Group Databasebeta

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C2×C11×D181⋊C3 #37560669

order23892
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D181⋊C3
unambiguous semidirect productD181⋊(C2×C3×C11)
unambiguous semidirect product(C181⋊C3)⋊(C22×C11)
unambiguous semidirect product(C2×D181)⋊(C3×C11)
unambiguous semidirect product(C2×C181⋊C3)⋊(C2×C11)
unambiguous semidirect product(C2×C11×D181)⋊C3

Splittings

Fitting, socleC2×C11×C181 ⋊ C2×C3
derived, SylowC181 ⋊ C22×C3×C11
HallC2×C11×D181 ⋊ C3
HallC11×C181⋊C3 ⋊ C22
HallC11×C181 ⋊ C22×C3
HallC2×D181 ⋊ C3×C11
HallC181⋊C3 ⋊ C22×C11

Subgroups

subgroupG/H
center, hypercenterC2×C11D181⋊C3
commutator, cosocle, hypocenterC181C22×C3×C11
FrattiniC1G
Fitting, socleC2×C11×C181C2×C3
LCSG ▷ C181
UCSC1 ◁ C2×C11

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3982

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23892, 17);