Finite Group Databasebeta

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C2×C11×D11×C49 #37557384

order23716
automorphism?
homologyAbelianization (H1) = C22×C11×C49 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D11×C49
unambiguous semidirect productC11⋊(C22×C11×C49)
unambiguous semidirect product(C2×C11)⋊(C2×C11×C49)

Splittings

FittingC2×C112×C49 ⋊ C2
derivedC11 ⋊ C22×C11×C49
HallC112×C49 ⋊ C22
SylowC112 ⋊ C22×C49

Subgroups

subgroupG/H
center, hypercenterC2×C11×C49D11
commutator, hypocenterC11C22×C11×C49
FrattiniC7C2×C7×C11×D11
FittingC2×C112×C49C2
socleC2×C7×C112C2×C7
prime radicalC2×C7×C11×D11C7
cosocleC7×C11C22×C7×C11
LCSG ▷ C11
UCSC1 ◁ C2×C11×C49

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2156

Conjugacy classes & character table

7546 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23716, 47);