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C7×D17×ΓL(1,𝔽32) #49146271

order36890
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D17×ΓL(1,𝔽32)
unambiguous semidirect productC17⋊(C2×C7×ΓL(1,𝔽32))
unambiguous semidirect product(C31×D17)⋊(C5×C7)
unambiguous semidirect product(C7×C31×D17)⋊C5

Splittings

Fitting, socle, HallC7×C17×C31 ⋊ C2×C5
derived, HallC17×C31 ⋊ C2×C5×C7
HallC7×C17×ΓL(1,𝔽32) ⋊ C2
HallC7×C31×D17 ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ C2×C7
HallC31×D17 ⋊ C5×C7
HallC7×C31 ⋊ C5×D17
HallC7×C17 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ C5×C7×D17
SylowC17 ⋊ C2×C7×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC7D17×ΓL(1,𝔽32)
commutator, cosocle, hypocenterC17×C31C2×C5×C7
FrattiniC1G
Fitting, socleC7×C17×C31C2×C5
LCSG ▷ C17×C31
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3689

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36890, 19);