Finite Group Databasebeta

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C2×C11×#13109901 #49114433

order36036
automorphism?
homologyAbelianization (H1) = C22×C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×#13109901

Splittings

derived, HallC7×C13 ⋊ C22×C9×C11
HallC11×#11717942 ⋊ C22
HallC2×C11×C13×D7 ⋊ C9
HallC7×C11×C13 ⋊ C22×C9
Hall#11717942 ⋊ C22×C11
HallC2×C13×D7 ⋊ C9×C11
HallC2×C11×D7 ⋊ C13⋊C9
HallC11×C13 ⋊ C2×D7⋊C9
HallC7×C11 ⋊ C22×C13⋊C9
HallC2×D7 ⋊ C11×C13⋊C9
SylowC13 ⋊ C2×C11×D7⋊C9
SylowC7 ⋊ C22×C11×C13⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11#10587721
commutator, hypocenterC7×C13C22×C9×C11
FrattiniC3C2×C11×#10587721
Fitting, socleC2×C3×C7×C11×C13C2×C3
prime radicalC2×C3×C11×C13×D7C3
cosocleC3×C7×C13C22×C3×C11
LCSG ▷ C7×C13
UCSC1 ◁ C2×C3×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18018

Conjugacy classes & character table

1782 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 101);