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C7⋊C9×Dic11⋊C5 #28357367

order13860
automorphism?
homologyAbelianization (H1) = C4×C5×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(C7×Dic11⋊C5)⋊C9
unambiguous semidirect product(Dic11×C7⋊C9)⋊C5

Splittings

derived, HallC7×C11 ⋊ C4×C5×C9
HallC11⋊C5×C7⋊C9 ⋊ C4
HallDic11×C7⋊C9 ⋊ C5
HallC7×Dic11⋊C5 ⋊ C9
HallC11×C7⋊C9 ⋊ C4×C5
HallC7×C11⋊C5 ⋊ C4×C9
HallC7×Dic11 ⋊ C5×C9
HallC11⋊C5 ⋊ C4×C7⋊C9
HallDic11 ⋊ C5×C7⋊C9
SylowC11 ⋊ C4×C5×C7⋊C9
SylowC7 ⋊ C9×Dic11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC2×C3ΓL(1,𝔽8)×AGL(1,𝔽11)
commutator, hypocenterC7×C11C4×C5×C9
Fitting, socle, cosocleC2×C3×C7×C11C2×C3×C5
prime radicalC2×C3×C7×C11⋊C5C2×C3
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13860, 34);