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C9×C7⋊(Dic11⋊C5) #28357355

order13860
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×C7⋊(Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊(C9×Dic7)
unambiguous semidirect product(C9×Dic77)⋊C5

Splittings

derived, HallC7×C11 ⋊ C4×C5×C9
HallC7×C9×C11⋊C5 ⋊ C4
HallC9×Dic77 ⋊ C5
HallC7×C9×C11 ⋊ C4×C5
HallC9×C11⋊C5 ⋊ Dic7
HallC7×C11⋊C5 ⋊ C4×C9
HallDic77 ⋊ C5×C9
HallC9×C11 ⋊ C5×Dic7
HallC7×C9 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C9×Dic7
SylowC11 ⋊ C5×C9×Dic7
SylowC7 ⋊ C9×Dic11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C9C7⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C4×C5×C9
FrattiniC2×C3C3×C7⋊AGL(1,𝔽11)
FittingC2×C7×C9×C11C2×C5
socle, cosocleC2×C3×C7×C11C2×C3×C5
prime radicalC2×C3×C7×C11⋊C5C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C2×C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 22);