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C17×C7⋊(D31⋊C5) #49146274

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

Aliases

direct productC17×C7⋊(D31⋊C5)
unambiguous semidirect productC7⋊(C17×D31⋊C5)
unambiguous semidirect productΓL(1,𝔽32)⋊(D7×C17)
unambiguous semidirect productD217⋊(C5×C17)
unambiguous semidirect product(C17×D217)⋊C5

Splittings

Fitting, socle, HallC7×C17×C31 ⋊ C2×C5
derived, HallC7×C31 ⋊ C2×C5×C17
HallC7×C17×ΓL(1,𝔽32) ⋊ C2
HallC17×D217 ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ D7
HallC7×ΓL(1,𝔽32) ⋊ C2×C17
HallC17×C31 ⋊ C5×D7
HallD217 ⋊ C5×C17
HallΓL(1,𝔽32) ⋊ D7×C17
HallC7×C17 ⋊ D31⋊C5
SylowC31 ⋊ C5×D7×C17
SylowC7 ⋊ C17×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC17C7⋊(D31⋊C5)
commutator, cosocle, hypocenterC7×C31C2×C5×C17
FrattiniC1G
Fitting, socleC7×C17×C31C2×C5
LCSG ▷ C7×C31
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3689

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36890, 22);