Finite Group Databasebeta

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C2×C32×C7×C13×D11 #49115010

order36036
automorphism?
homologyAbelianization (H1) = C22×C32×C7×C13 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×C7×C13×D11
unambiguous semidirect productC11⋊(C22×C32×C7×C13)
unambiguous semidirect product(C2×C11)⋊(C2×C32×C7×C13)

Splittings

Fitting, socleC2×C32×C7×C11×C13 ⋊ C2
derived, SylowC11 ⋊ C22×C32×C7×C13
HallC32×C7×C11×C13 ⋊ C22
HallC32×C11×C13 ⋊ C22×C7
HallC7×C11×C13 ⋊ C22×C32
HallC32×C7×C11 ⋊ C22×C13
HallC11×C13 ⋊ C22×C32×C7
HallC32×C11 ⋊ C22×C7×C13
HallC7×C11 ⋊ C22×C32×C13

Subgroups

subgroupG/H
center, hypercenterC2×C32×C7×C13D11
commutator, cosocle, hypocenterC11C22×C32×C7×C13
FrattiniC1G
Fitting, socleC2×C32×C7×C11×C13C2
LCSG ▷ C11
UCSC1 ◁ C2×C32×C7×C13

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18018

Conjugacy classes & character table

11466 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 678);