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C17×AGL(1,𝔽5)×C7⋊C9 #36339201

order21420
automorphism?
homologyAbelianization (H1) = C4×C9×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×AGL(1,𝔽5)×C7⋊C9
unambiguous semidirect product(C7×AGL(1,𝔽5))⋊(C9×C17)
unambiguous semidirect product(C7×C17×AGL(1,𝔽5))⋊C9

Splittings

derived, HallC5×C7 ⋊ C4×C9×C17
HallC5×C17×C7⋊C9 ⋊ C4
HallC7×C17×AGL(1,𝔽5) ⋊ C9
HallC5×C7×C17 ⋊ C4×C9
HallC5×C7⋊C9 ⋊ C4×C17
HallC7×AGL(1,𝔽5) ⋊ C9×C17
HallC7×C17 ⋊ C9×AGL(1,𝔽5)
HallC5×C17 ⋊ C4×C7⋊C9
SylowC7 ⋊ C9×C17×AGL(1,𝔽5)
SylowC5 ⋊ C4×C17×C7⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C17AGL(1,𝔽5)×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C4×C9×C17
FrattiniC3C17×AGL(1,𝔽5)×ΓL(1,𝔽8)
Fitting, socleC3×C5×C7×C17C3×C4
prime radicalC3×C7×D5×C17C2×C3
cosocleC3×C7×D5C2×C3×C17
LCSG ▷ C5×C7
UCSC1 ◁ C3×C17

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5355

Conjugacy classes & character table

1275 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 33);