Finite Group Databasebeta

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C2×C3×C11×C157⋊C3 #44527274

order31086
automorphism?
homologyAbelianization (H1) = C2×C32×C11 · Schur multiplier (H2) = C3

Aliases

direct productC2×C3×C11×C157⋊C3
unambiguous semidirect product(C2×C157)⋊(C32×C11)
unambiguous semidirect product(C2×C3×C157)⋊(C3×C11)
unambiguous semidirect product(C2×C11×C157)⋊C32
unambiguous semidirect product(C2×C3×C11×C157)⋊C3

Splittings

Fitting, socleC2×C3×C11×C157 ⋊ C3
derived, SylowC157 ⋊ C2×C32×C11
HallC2×C11×C157 ⋊ C32
HallC11×C157 ⋊ C2×C32
HallC2×C157 ⋊ C32×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11C157⋊C3
commutator, cosocle, hypocenterC157C2×C32×C11
FrattiniC1G
Fitting, socleC2×C3×C11×C157C3
LCSG ▷ C157
UCSC1 ◁ C2×C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10362

Conjugacy classes & character table

3630 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31086, 21);