Finite Group Databasebeta

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C2×C5×C11×D7⋊C9 #28357403

order13860
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C22×C5×C9×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C11×D7⋊C9
unambiguous semidirect productD7⋊(C2×C5×C9×C11)
unambiguous semidirect product(C2×D7)⋊(C5×C9×C11)
unambiguous semidirect product(C7⋊C9)⋊(C22×C5×C11)
unambiguous semidirect product(C2×C7⋊C9)⋊(C2×C5×C11)
unambiguous semidirect product(C2×C5×D7)⋊(C9×C11)
unambiguous semidirect product(C2×C5×C11×D7)⋊C9

Splittings

derived, SylowC7 ⋊ C22×C5×C9×C11
HallC5×C11×C7⋊C9 ⋊ C22
HallC2×C5×C11×D7 ⋊ C9
HallC11×C7⋊C9 ⋊ C22×C5
HallC5×C7×C11 ⋊ C22×C9
HallC5×C7⋊C9 ⋊ C22×C11
HallC2×C11×D7 ⋊ C5×C9
HallC2×C5×D7 ⋊ C9×C11
HallC7×C11 ⋊ C22×C5×C9
HallC7⋊C9 ⋊ C22×C5×C11
HallC5×C7 ⋊ C22×C9×C11
HallC2×D7 ⋊ C5×C9×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C11AGL(1,𝔽7)
commutator, hypocenterC7C22×C5×C9×C11
FrattiniC3C2×C5×C11×AGL(1,𝔽7)
Fitting, socleC2×C3×C5×C7×C11C2×C3
prime radicalC2×C3×C5×C11×D7C3
cosocleC3×C7C22×C3×C5×C11
LCSG ▷ C7
UCSC1 ◁ C2×C3×C5×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6930

Conjugacy classes & character table

2310 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 70);