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C2×C7×C17×ΓL(1,𝔽32) #49146254

order36890
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C17 · Schur multiplier (H2) = C1

Aliases

direct productC2×C7×C17×ΓL(1,𝔽32)
unambiguous semidirect product(C2×C31)⋊(C5×C7×C17)
unambiguous semidirect product(C2×C7×C31)⋊(C5×C17)
unambiguous semidirect product(C2×C17×C31)⋊(C5×C7)
unambiguous semidirect product(C2×C7×C17×C31)⋊C5

Splittings

Fitting, socle, HallC2×C7×C17×C31 ⋊ C5
derived, SylowC31 ⋊ C2×C5×C7×C17
HallC7×C17×C31 ⋊ C2×C5
HallC2×C17×C31 ⋊ C5×C7
HallC17×C31 ⋊ C2×C5×C7
HallC2×C7×C31 ⋊ C5×C17
HallC7×C31 ⋊ C2×C5×C17
HallC2×C31 ⋊ C5×C7×C17

Subgroups

subgroupG/H
center, hypercenterC2×C7×C17ΓL(1,𝔽32)
commutator, cosocle, hypocenterC31C2×C5×C7×C17
FrattiniC1G
Fitting, socleC2×C7×C17×C31C5
LCSG ▷ C31
UCSC1 ◁ C2×C7×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7378

Conjugacy classes & character table

2618 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36890, 2);