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C31×C5⋊(D19⋊C3) #31798997

order17670
automorphism?
homologyAbelianization (H1) = C2×C3×C31 · Schur multiplier (H2) = C1

Aliases

direct productC31×C5⋊(D19⋊C3)
unambiguous semidirect productC5⋊(C31×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(D5×C31)
unambiguous semidirect productD95⋊(C3×C31)

Splittings

Fitting, socle, HallC5×C19×C31 ⋊ C2×C3
derived, HallC5×C19 ⋊ C2×C3×C31
HallC5×C31×C19⋊C3 ⋊ C2
HallC31×D95 ⋊ C3
HallC31×C19⋊C3 ⋊ D5
HallC19×C31 ⋊ C3×D5
HallC5×C19⋊C3 ⋊ C2×C31
HallD95 ⋊ C3×C31
HallC5×C31 ⋊ D19⋊C3
HallC19⋊C3 ⋊ D5×C31
SylowC19 ⋊ C3×D5×C31
SylowC5 ⋊ C31×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC31C5⋊(D19⋊C3)
commutator, cosocle, hypocenterC5×C19C2×C3×C31
FrattiniC1G
Fitting, socleC5×C19×C31C2×C3
LCSG ▷ C5×C19
UCSC1 ◁ C31

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2945

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD31×C5⋊(D19⋊C3), D5×C31×D19⋊C3, (C5⋊(D19⋊C3))⋊D31, …
maximal normal subgroup ofD31×C5⋊(D19⋊C3), D5×C31×D19⋊C3, (C5⋊(D19⋊C3))⋊D31, …
maximal quotient ofC31×(C19⋊C3)⋊Dic5, C2×C31×C5⋊(D19⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17670, 54);