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C5×C11⋊(Dic7⋊C9) #28357362

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

Aliases

direct productC5×C11⋊(Dic7⋊C9)
unambiguous semidirect product(C7⋊C9)⋊(C5×Dic11)
unambiguous semidirect product(C5×Dic77)⋊C9

Splittings

derived, HallC7×C11 ⋊ C4×C5×C9
HallC5×C11×C7⋊C9 ⋊ C4
HallC5×Dic77 ⋊ C9
HallC11×C7⋊C9 ⋊ C4×C5
HallC5×C7×C11 ⋊ C4×C9
HallC5×C7⋊C9 ⋊ Dic11
HallDic77 ⋊ C5×C9
HallC7⋊C9 ⋊ C5×Dic11
HallC5×C11 ⋊ Dic7⋊C9
HallC5×C7 ⋊ C9×Dic11
SylowC11 ⋊ C5×Dic7⋊C9
SylowC7 ⋊ C5×C9×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C11⋊AGL(1,𝔽7)
commutator, hypocenterC7×C11C4×C5×C9
FrattiniC2×C3C5×C11⋊AGL(1,𝔽7)
Fitting, socle, prime radicalC2×C3×C5×C7×C11C2×C3
cosocleC2×C3×C7×C11C2×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13860

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, 29);