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C7×C17×C9⋊AGL(1,𝔽5) #36339247

order21420
automorphism?
homologyAbelianization (H1) = C4×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC7×C17×C9⋊AGL(1,𝔽5)
unambiguous semidirect productC9⋊(C7×C17×AGL(1,𝔽5))

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC7×C17C9⋊AGL(1,𝔽5)
commutator, hypocenterC5×C9C4×C7×C17
FrattiniC3C7×C17×ΓL(1,𝔽16)
FittingC5×C7×C9×C17C4
socleC3×C5×C7×C17Dic3
prime radicalC3×C7×D5×C17D3
cosocleC9×D5C2×C7×C17
LCSG ▷ C5×C9
UCSC1 ◁ C7×C17

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5355

Conjugacy classes & character table

2499 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 79);