Finite Group Databasebeta

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C2×C7×C11×C3⋊D39 #49115025

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

Aliases

direct productC2×C7×C11×C3⋊D39
unambiguous semidirect product(C2×C3)⋊(C7×C11×D39)
unambiguous semidirect product(C2×C13)⋊(C7×C11×C3⋊D3)

Splittings

Fitting, socleC2×C32×C7×C11×C13 ⋊ C2
derived, HallC32×C13 ⋊ C22×C7×C11
HallC32×C7×C11×C13 ⋊ C22
HallC32×C11×C13 ⋊ C22×C7
HallC7×C11×C13 ⋊ C2×C3⋊D3
HallC32×C7×C13 ⋊ C22×C11
HallC32×C7×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C7×C3⋊D3
HallC32×C11 ⋊ C2×C7×D13
HallC7×C13 ⋊ C2×C11×C3⋊D3
HallC32×C7 ⋊ C2×C11×D13
SylowC13 ⋊ C2×C7×C11×C3⋊D3
SylowC32 ⋊ C2×C7×C11×D13

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11C3⋊D39
commutator, cosocle, hypocenterC32×C13C22×C7×C11
FrattiniC1G
Fitting, socleC2×C32×C7×C11×C13C2
LCSG ▷ C32×C13
UCSC1 ◁ C2×C7×C11

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18018

Conjugacy classes & character table

9240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 693);