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C9×C7⋊#66776 #36339229

order21420
automorphism?
homologyAbelianization (H1) = C4×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×C7⋊#66776

Splittings

Fitting, HallC5×C7×C9×C17 ⋊ C4
derived, HallC5×C7×C17 ⋊ C4×C9
HallC7×C9×C17 ⋊ AGL(1,𝔽5)
HallC5×C9×C17 ⋊ Dic7
HallC5×C7×C9 ⋊ #595
HallC9×C17 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C17 ⋊ C9×AGL(1,𝔽5)
HallC5×C17 ⋊ C9×Dic7
HallC7×C9 ⋊ #66776
HallC5×C9 ⋊ C7⋊#595
HallC5×C7 ⋊ C9×#595
SylowC17 ⋊ C9×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ C9×#66776
SylowC5 ⋊ C9×C7⋊#595

Subgroups

subgroupG/H
center, hypercenterC9C7⋊#66776
commutator, hypocenterC5×C7×C17C4×C9
FrattiniC3C3×C7⋊#66776
FittingC5×C7×C9×C17C4
socleC3×C5×C7×C17C3×C4
prime radical, cosocleC3×C7×D85C2×C3
LCSG ▷ C5×C7×C17
UCSC1 ◁ C9

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5355

Conjugacy classes & character table

1413 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 61);