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C19×C5⋊(D31⋊C3) #31798992

order17670
automorphism?
homologyAbelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×C5⋊(D31⋊C3)
unambiguous semidirect productC5⋊(C19×D31⋊C3)
unambiguous semidirect product(C31⋊C3)⋊(D5×C19)
unambiguous semidirect productD155⋊(C3×C19)

Splittings

Fitting, socle, HallC5×C19×C31 ⋊ C2×C3
derived, HallC5×C31 ⋊ C2×C3×C19
HallC5×C19×C31⋊C3 ⋊ C2
HallC19×D155 ⋊ C3
HallC19×C31⋊C3 ⋊ D5
HallC19×C31 ⋊ C3×D5
HallC5×C31⋊C3 ⋊ C2×C19
HallD155 ⋊ C3×C19
HallC5×C19 ⋊ D31⋊C3
HallC31⋊C3 ⋊ D5×C19
SylowC31 ⋊ C3×D5×C19
SylowC5 ⋊ C19×D31⋊C3

Subgroups

subgroupG/H
center, hypercenterC19C5⋊(D31⋊C3)
commutator, cosocle, hypocenterC5×C31C2×C3×C19
FrattiniC1G
Fitting, socleC5×C19×C31C2×C3
LCSG ▷ C5×C31
UCSC1 ◁ C19

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2945

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD5×C19×D31⋊C3, D19×C5⋊(D31⋊C3), (C5⋊(D31⋊C3))⋊D19, …
maximal normal subgroup ofD5×C19×D31⋊C3, D19×C5⋊(D31⋊C3), (C5⋊(D31⋊C3))⋊D19, …
maximal quotient ofC19×(C31⋊C3)⋊Dic5, C2×C19×C5⋊(D31⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17670, 49);