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C7×C9×Dic11⋊C5 #28357353

order13860
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C4×C5×C7×C9 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×Dic11⋊C5
unambiguous semidirect productDic11⋊(C5×C7×C9)
unambiguous semidirect product(C11⋊C5)⋊(C4×C7×C9)
unambiguous semidirect product(C9×Dic11)⋊(C5×C7)
unambiguous semidirect product(C7×C9×Dic11)⋊C5

Splittings

derived, SylowC11 ⋊ C4×C5×C7×C9
HallC7×C9×C11⋊C5 ⋊ C4
HallC7×C9×Dic11 ⋊ C5
HallC7×C9×C11 ⋊ C4×C5
HallC9×C11⋊C5 ⋊ C4×C7
HallC9×Dic11 ⋊ C5×C7
HallC7×C11⋊C5 ⋊ C4×C9
HallC7×Dic11 ⋊ C5×C9
HallC9×C11 ⋊ C4×C5×C7
HallC7×C11 ⋊ C4×C5×C9
HallC11⋊C5 ⋊ C4×C7×C9
HallDic11 ⋊ C5×C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C7×C9AGL(1,𝔽11)
commutator, hypocenterC11C4×C5×C7×C9
FrattiniC2×C3C3×C7×AGL(1,𝔽11)
FittingC2×C7×C9×C11C2×C5
socleC2×C3×C7×C11C2×C3×C5
prime radicalC2×C3×C7×C11⋊C5C2×C3
cosocleC2×C3×C11C2×C3×C5×C7
LCSG ▷ C11
UCSC1 ◁ C2×C7×C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Conjugacy classes & character table

1386 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 20);