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C3×D17×ΓL(1,𝔽32) #30629040

order15810
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×D17×ΓL(1,𝔽32)
unambiguous semidirect productC17⋊(C2×C3×ΓL(1,𝔽32))
unambiguous semidirect product(C3×C31×D17)⋊C5

Splittings

Fitting, socle, HallC3×C17×C31 ⋊ C2×C5
derived, HallC17×C31 ⋊ C2×C3×C5
HallC3×C17×ΓL(1,𝔽32) ⋊ C2
HallC3×C31×D17 ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ C2×C3
HallC31×D17 ⋊ C3×C5
HallC3×C31 ⋊ C5×D17
HallC3×C17 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C3×C5×D17
SylowC17 ⋊ C2×C3×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC3D17×ΓL(1,𝔽32)
commutator, cosocle, hypocenterC17×C31C2×C3×C5
FrattiniC1G
Fitting, socleC3×C17×C31C2×C5
LCSG ▷ C17×C31
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1581

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×ΓL(1,𝔽32)⋊#595, C3×#595×ΓL(1,𝔽32), C3×D17×D31⋊C5, …
maximal normal subgroup ofC3×ΓL(1,𝔽32)⋊#595, C3×#595×ΓL(1,𝔽32), C3×D17×D31⋊C5, …
maximal quotient ofC3×Dic17×ΓL(1,𝔽32), C2×C3×D17×ΓL(1,𝔽32)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15810, 21);