Finite Group Databasebeta

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C2×C5×C11⋊(D7⋊C9) #28357404

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

Aliases

direct productC2×C5×C11⋊(D7⋊C9)
unambiguous semidirect product(C2×C7⋊C9)⋊(C5×D11)
unambiguous semidirect product(C2×C5×D77)⋊C9

Splittings

derived, HallC7×C11 ⋊ C22×C5×C9
HallC5×C11×C7⋊C9 ⋊ C22
HallC2×C5×D77 ⋊ C9
HallC11×C7⋊C9 ⋊ C22×C5
HallC5×C7×C11 ⋊ C22×C9
HallC5×C7⋊C9 ⋊ C2×D11
HallC2×D77 ⋊ 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, hypercenterC2×C3×C5C11⋊AGL(1,𝔽7)
commutator, hypocenterC7×C11C22×C5×C9
FrattiniC3C2×C5×C11⋊AGL(1,𝔽7)
Fitting, socleC2×C3×C5×C7×C11C2×C3
prime radicalC2×C3×C5×D77C3
cosocleC3×C7×C11C22×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C5

120 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 58 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) = 6930

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 71);