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C22×C11×#11717942 #49114503

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

Aliases

direct productC22×C11×#11717942

Splittings

derived, HallC7×C13 ⋊ C22×C9×C11
HallC22×C7×C11×C13 ⋊ C9
HallC7×C11×C13 ⋊ C22×C9
HallC22×C11×C13 ⋊ C7⋊C9
HallC22×C7×C13 ⋊ C9×C11
HallC22×C7×C11 ⋊ C13⋊C9
HallC11×C13 ⋊ C22×C7⋊C9
HallC7×C11 ⋊ C22×C13⋊C9
HallC22×C13 ⋊ C11×C7⋊C9
HallC22×C7 ⋊ C11×C13⋊C9
SylowC13 ⋊ C22×C11×C7⋊C9
SylowC7 ⋊ C22×C11×C13⋊C9

Subgroups

subgroupG/H
center, hypercenterC22×C3×C11#63271
commutator, hypocenterC7×C13C22×C9×C11
FrattiniC3C22×C11×#63271
Fitting, socle, prime radicalC22×C3×C7×C11×C13C3
cosocleC3×C7×C13C22×C3×C11
LCSG ▷ C7×C13
UCSC1 ◁ C22×C3×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36036

Conjugacy classes & character table

4356 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 171);