Finite Group Databasebeta

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C2×C13×C11⋊(D7⋊C9) #49114435

order36036
automorphism?
homologyAbelianization (H1) = C22×C9×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×C11⋊(D7⋊C9)
unambiguous semidirect product(C2×C11)⋊(C13×D7⋊C9)
unambiguous semidirect product(C2×C7⋊C9)⋊(C13×D11)
unambiguous semidirect product(C2×D77)⋊(C9×C13)

Splittings

derived, HallC7×C11 ⋊ C22×C9×C13
HallC11×C13×C7⋊C9 ⋊ C22
HallC2×C13×D77 ⋊ C9
HallC7×C11×C13 ⋊ C22×C9
HallC13×C7⋊C9 ⋊ C2×D11
HallC11×C7⋊C9 ⋊ C22×C13
HallC2×D77 ⋊ C9×C13
HallC11×C13 ⋊ C2×D7⋊C9
HallC7×C13 ⋊ C2×C9×D11
HallC7⋊C9 ⋊ C2×C13×D11
SylowC11 ⋊ C2×C13×D7⋊C9
SylowC7 ⋊ C2×C9×C13×D11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13C11⋊AGL(1,𝔽7)
commutator, hypocenterC7×C11C22×C9×C13
FrattiniC3C2×C13×C11⋊AGL(1,𝔽7)
Fitting, socleC2×C3×C7×C11×C13C2×C3
prime radicalC2×C3×C13×D77C3
cosocleC3×C7×C11C22×C3×C13
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C13

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18018

Conjugacy classes & character table

2496 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 103);