Finite Group Databasebeta

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C2×C11⋊#13109896 #49114445

order36036
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11⋊#13109896
unambiguous semidirect product(C2×C11)⋊#13109896

Splittings

derived, HallC7×C11×C13 ⋊ C22×C9
HallC11×#11717941 ⋊ C22
HallC2×C7×D143 ⋊ C9
Hall#11717941 ⋊ C2×D11
HallC2×D143 ⋊ C7⋊C9
HallC11×C13 ⋊ C22×C7⋊C9
HallC7×C13 ⋊ C2×C9×D11
HallC7×C11 ⋊ C2×D13⋊C9
SylowC13 ⋊ C2×D11×C7⋊C9
SylowC11 ⋊ C2×#13109896
SylowC7 ⋊ C2×C11⋊(D13⋊C9)

Subgroups

subgroupG/H
center, hypercenterC2×C3C11⋊#10587716
commutator, hypocenterC7×C11×C13C22×C9
FrattiniC3C2×C11⋊#10587716
Fitting, socleC2×C3×C7×C11×C13C2×C3
prime radicalC2×C3×C7×D143C3
cosocleC3×C7×C11×C13C22×C3
LCSG ▷ C7×C11×C13
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18018

Conjugacy classes & character table

1134 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 113);