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D5×C17×C37⋊C3 #34038280

order18870
automorphism?
homologyAbelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1

Aliases

direct productD5×C17×C37⋊C3
unambiguous semidirect productC5⋊(C2×C17×C37⋊C3)
unambiguous semidirect product(D5×C37)⋊(C3×C17)
unambiguous semidirect product(D5×C17×C37)⋊C3

Splittings

Fitting, socle, HallC5×C17×C37 ⋊ C2×C3
derived, HallC5×C37 ⋊ C2×C3×C17
HallC5×C17×C37⋊C3 ⋊ C2
HallD5×C17×C37 ⋊ C3
HallC17×C37 ⋊ C3×D5
HallC5×C37⋊C3 ⋊ C2×C17
HallD5×C37 ⋊ C3×C17
HallC5×C17 ⋊ C2×C37⋊C3
SylowC37 ⋊ C3×D5×C17
SylowC5 ⋊ C2×C17×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC17D5×C37⋊C3
commutator, cosocle, hypocenterC5×C37C2×C3×C17
FrattiniC1G
Fitting, socleC5×C17×C37C2×C3
LCSG ▷ C5×C37
UCSC1 ◁ C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3145

Conjugacy classes & character table

1020 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC17×#10625193⋊C3, C17×AGL(1,𝔽5)×C37⋊C3, #27160380⋊C3, …
maximal normal subgroup ofC17×#10625193⋊C3, C17×AGL(1,𝔽5)×C37⋊C3, #27160380⋊C3, …
maximal quotient ofC17×Dic5×C37⋊C3, C2×D5×C17×C37⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18870, 21);