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C7×C9⋊#66775 #36339248

order21420
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9⋊#66775
unambiguous semidirect productC9⋊(C7×#66775)

Splittings

Fitting, HallC5×C7×C9×C17 ⋊ C4
derived, HallC5×C9×C17 ⋊ C4×C7
HallC7×C9×C17 ⋊ AGL(1,𝔽5)
HallC5×C7×C17 ⋊ Dic9
HallC5×C7×C9 ⋊ #595
HallC9×C17 ⋊ C7×AGL(1,𝔽5)
HallC7×C17 ⋊ C9⋊AGL(1,𝔽5)
HallC5×C17 ⋊ C7×Dic9
HallC7×C9 ⋊ #66775
HallC5×C9 ⋊ C7×#595
HallC5×C7 ⋊ C9⋊#595
SylowC17 ⋊ C7×C9⋊AGL(1,𝔽5)
SylowC9 ⋊ C7×#66775
SylowC5 ⋊ C7×C9⋊#595

Subgroups

subgroupG/H
center, hypercenterC7C9⋊#66775
commutator, hypocenterC5×C9×C17C4×C7
FrattiniC3C7×C3⋊#66775
FittingC5×C7×C9×C17C4
socleC3×C5×C7×C17Dic3
prime radicalC3×C7×D85D3
cosocleC9×D85C2×C7
LCSG ▷ C5×C9×C17
UCSC1 ◁ C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5355

Conjugacy classes & character table

1407 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 80);