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C9×AGL(1,𝔽53) #37613586

order24804
automorphism?
homologyAbelianization (H1) = C4×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC9×AGL(1,𝔽53)
unambiguous semidirect product#6157⋊(C9×C13)
unambiguous semidirect product(C9×#6157)⋊C13

Splittings

Fitting, HallC9×C53 ⋊ C4×C13
derived, SylowC53 ⋊ C4×C9×C13
HallC9×C53⋊C13 ⋊ C4
HallC9×#6157 ⋊ C13
HallC53⋊C13 ⋊ C4×C9
Hall#6157 ⋊ C9×C13

Subgroups

subgroupG/H
center, hypercenterC9AGL(1,𝔽53)
commutator, hypocenterC53C4×C9×C13
FrattiniC3C3×AGL(1,𝔽53)
FittingC9×C53C4×C13
socleC3×C53C3×C4×C13
prime radicalC3×D53⋊C13C2×C3
cosocleC3×D53C2×C3×C13
LCSG ▷ C53
UCSC1 ◁ C9

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 477

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 18);