Finite Group Databasebeta

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C5×D11×D7⋊C9 #28357385

order13860
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC5×D11×D7⋊C9
unambiguous semidirect productD7⋊(C5×C9×D11)
unambiguous semidirect product(C5×D7×D11)⋊C9

Splittings

derived, HallC7×C11 ⋊ C22×C5×C9
HallC5×C11×C7⋊C9 ⋊ C22
HallC5×D7×D11 ⋊ C9
HallC11×C7⋊C9 ⋊ C22×C5
HallC5×C7×C11 ⋊ C22×C9
HallC5×C7⋊C9 ⋊ C2×D11
HallD7×D11 ⋊ C5×C9
HallC7⋊C9 ⋊ C2×C5×D11
HallC5×C11 ⋊ C2×D7⋊C9
HallC5×C7 ⋊ C2×C9×D11
SylowC11 ⋊ C2×C5×D7⋊C9
SylowC7 ⋊ C2×C5×C9×D11

Subgroups

subgroupG/H
center, hypercenterC3×C5D11×AGL(1,𝔽7)
commutator, hypocenterC7×C11C22×C5×C9
FrattiniC3C5×D11×AGL(1,𝔽7)
Fitting, socleC3×C5×C7×C11C22×C3
prime radicalC3×C5×D7×D11C3
cosocleC3×C7×C11C22×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C3×C5

120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3465

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 52);