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C3×C4×C17×ΓL(1,𝔽32) #44539245

order31620
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C4×C17×ΓL(1,𝔽32)
unambiguous semidirect product(C3×C4×C31)⋊(C5×C17)
unambiguous semidirect product(C3×C4×C17×C31)⋊C5

Splittings

Fitting, HallC3×C4×C17×C31 ⋊ C5
derived, SylowC31 ⋊ C3×C4×C5×C17
HallC4×C17×C31 ⋊ C3×C5
HallC3×C17×C31 ⋊ C4×C5
HallC17×C31 ⋊ C3×C4×C5
HallC3×C4×C31 ⋊ C5×C17
HallC4×C31 ⋊ C3×C5×C17
HallC3×C31 ⋊ C4×C5×C17

Subgroups

subgroupG/H
center, hypercenterC3×C4×C17ΓL(1,𝔽32)
commutator, hypocenterC31C3×C4×C5×C17
FrattiniC2C2×C3×C17×ΓL(1,𝔽32)
FittingC3×C4×C17×C31C5
socleC2×C3×C17×C31C2×C5
prime radicalC2×C3×C17×ΓL(1,𝔽32)C2
cosocleC2×C31C2×C3×C5×C17
LCSG ▷ C31
UCSC1 ◁ C3×C4×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6324

Conjugacy classes & character table

2244 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 2);