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Dic3×C17×ΓL(1,𝔽32) #44539266

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

Aliases

direct productDic3×C17×ΓL(1,𝔽32)
unambiguous semidirect productC3⋊(C4×C17×ΓL(1,𝔽32))
unambiguous semidirect product(Dic3×C31)⋊(C5×C17)
unambiguous semidirect product(Dic3×C17×C31)⋊C5

Splittings

derived, HallC3×C31 ⋊ C4×C5×C17
HallC3×C17×ΓL(1,𝔽32) ⋊ C4
HallDic3×C17×C31 ⋊ C5
HallC3×C17×C31 ⋊ C4×C5
HallC17×C31 ⋊ C5×Dic3
HallC3×ΓL(1,𝔽32) ⋊ C4×C17
HallDic3×C31 ⋊ C5×C17
HallC3×C17 ⋊ C4×ΓL(1,𝔽32)
SylowC31 ⋊ C5×Dic3×C17
SylowC3 ⋊ C4×C17×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC2×C17D3×ΓL(1,𝔽32)
commutator, hypocenterC3×C31C4×C5×C17
FrattiniC2D3×C17×ΓL(1,𝔽32)
Fitting, socleC2×C3×C17×C31C2×C5
prime radicalC2×C3×C17×ΓL(1,𝔽32)C2
cosocleC2×C3×C31C2×C5×C17
LCSG ▷ C3×C31
UCSC1 ◁ C2×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6324

Conjugacy classes & character table

1122 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 23);