Finite Group Databasebeta

← Prev (#49146269) Next (#49146271) →

C7×C17×D31⋊C5 #49146270

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

Aliases

direct productC7×C17×D31⋊C5
unambiguous semidirect productD31⋊(C5×C7×C17)
unambiguous semidirect productΓL(1,𝔽32)⋊(C2×C7×C17)
unambiguous semidirect product(C7×D31)⋊(C5×C17)
unambiguous semidirect product(C17×D31)⋊(C5×C7)
unambiguous semidirect product(C7×C17×D31)⋊C5

Splittings

Fitting, socle, HallC7×C17×C31 ⋊ C2×C5
derived, SylowC31 ⋊ C2×C5×C7×C17
HallC7×C17×ΓL(1,𝔽32) ⋊ C2
HallC7×C17×D31 ⋊ C5
HallC17×ΓL(1,𝔽32) ⋊ C2×C7
HallC7×ΓL(1,𝔽32) ⋊ C2×C17
HallC17×D31 ⋊ C5×C7
HallC17×C31 ⋊ C2×C5×C7
HallC7×D31 ⋊ C5×C17
HallC7×C31 ⋊ C2×C5×C17
HallΓL(1,𝔽32) ⋊ C2×C7×C17
HallD31 ⋊ C5×C7×C17

Subgroups

subgroupG/H
center, hypercenterC7×C17D31⋊C5
commutator, cosocle, hypocenterC31C2×C5×C7×C17
FrattiniC1G
Fitting, socleC7×C17×C31C2×C5
LCSG ▷ C31
UCSC1 ◁ C7×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3689

Conjugacy classes & character table

1547 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36890, 18);