Finite Group Databasebeta

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C22×C3×C7×C11×C13⋊C3 #49115005

order36036
automorphism?
homologyAbelianization (H1) = C22×C32×C7×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC22×C3×C7×C11×C13⋊C3

Splittings

Fitting, socleC22×C3×C7×C11×C13 ⋊ C3
derived, SylowC13 ⋊ C22×C32×C7×C11
HallC22×C7×C11×C13 ⋊ C32
HallC7×C11×C13 ⋊ C22×C32
HallC22×C11×C13 ⋊ C32×C7
HallC22×C7×C13 ⋊ C32×C11
HallC11×C13 ⋊ C22×C32×C7
HallC7×C13 ⋊ C22×C32×C11
HallC22×C13 ⋊ C32×C7×C11

Subgroups

subgroupG/H
center, hypercenterC22×C3×C7×C11C13⋊C3
commutator, cosocle, hypocenterC13C22×C32×C7×C11
FrattiniC1G
Fitting, socleC22×C3×C7×C11×C13C3
LCSG ▷ C13
UCSC1 ◁ C22×C3×C7×C11

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12012

Conjugacy classes & character table

6468 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 673);