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C5×(C19⋊C3)⋊D31 #31798985

order17670
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C19⋊C3)⋊D31
unambiguous semidirect product(C19⋊C3)⋊(C5×D31)

Splittings

Fitting, socle, HallC5×C19×C31 ⋊ C2×C3
derived, HallC19×C31 ⋊ C2×C3×C5
HallC5×C31×C19⋊C3 ⋊ C2
HallC5×D589 ⋊ C3
HallC31×C19⋊C3 ⋊ C2×C5
HallD589 ⋊ C3×C5
HallC5×C19⋊C3 ⋊ D31
HallC5×C31 ⋊ D19⋊C3
HallC5×C19 ⋊ C3×D31
HallC19⋊C3 ⋊ C5×D31
SylowC31 ⋊ C5×D19⋊C3
SylowC19 ⋊ C3×C5×D31

Subgroups

subgroupG/H
center, hypercenterC5(C19⋊C3)⋊D31
commutator, cosocle, hypocenterC19×C31C2×C3×C5
FrattiniC1G
Fitting, socleC5×C19×C31C2×C3
LCSG ▷ C19×C31
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2945

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D31×D19⋊C3, D5×(C19⋊C3)⋊D31, (C5⋊(D19⋊C3))⋊D31, …
maximal normal subgroup ofC5×D31×D19⋊C3, D5×(C19⋊C3)⋊D31, (C5⋊(D19⋊C3))⋊D31, …
maximal quotient ofC5×(C19⋊C3)⋊Dic31, C2×C5×(C19⋊C3)⋊D31

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17670, 42);