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C4×C13⋊C3×ΓL(1,𝔽32) #37563709

order24180
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C13⋊C3×ΓL(1,𝔽32)
unambiguous semidirect product(C4×C13)⋊(C3×ΓL(1,𝔽32))
unambiguous semidirect product(C4×C31×C13⋊C3)⋊C5

Splittings

Fitting, HallC4×C13×C31 ⋊ C3×C5
derived, HallC13×C31 ⋊ C3×C4×C5
HallC4×C13×ΓL(1,𝔽32) ⋊ C3
HallC4×C31×C13⋊C3 ⋊ C5
HallC13×ΓL(1,𝔽32) ⋊ C3×C4
HallC31×C13⋊C3 ⋊ C4×C5
HallC4×C31 ⋊ C5×C13⋊C3
HallC4×C13 ⋊ C3×ΓL(1,𝔽32)
SylowC31 ⋊ C4×C5×C13⋊C3
SylowC13 ⋊ C3×C4×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC4C13⋊C3×ΓL(1,𝔽32)
commutator, hypocenterC13×C31C3×C4×C5
FrattiniC2C2×C13⋊C3×ΓL(1,𝔽32)
FittingC4×C13×C31C3×C5
socle, cosocleC2×C13×C31C2×C3×C5
prime radicalC2×C13⋊C3×ΓL(1,𝔽32)C2
LCSG ▷ C13×C31
UCSC1 ◁ C4

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1612

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 8);