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C2×C19×(C31⋊C3)⋊C5 #31798950

order17670
isoclinismisoclinic class of (C31⋊C3)⋊C5
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC2×C19×(C31⋊C3)⋊C5
unambiguous semidirect product(C2×C31⋊C3)⋊(C5×C19)
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊(C3×C19)
unambiguous semidirect product(C2×C19×C31⋊C3)⋊C5

Splittings

Fitting, socle, HallC2×C19×C31 ⋊ C3×C5
derived, SylowC31 ⋊ C2×C3×C5×C19
HallC2×C19×ΓL(1,𝔽32) ⋊ C3
HallC2×C19×C31⋊C3 ⋊ C5
HallC19×ΓL(1,𝔽32) ⋊ C2×C3
HallC19×C31⋊C3 ⋊ C2×C5
HallC19×C31 ⋊ C2×C3×C5
HallC2×ΓL(1,𝔽32) ⋊ C3×C19
HallC2×C31⋊C3 ⋊ C5×C19
HallΓL(1,𝔽32) ⋊ C2×C3×C19
HallC31⋊C3 ⋊ C2×C5×C19
HallC2×C31 ⋊ C3×C5×C19

Subgroups

subgroupG/H
center, hypercenterC2×C19(C31⋊C3)⋊C5
commutator, cosocle, hypocenterC31C2×C3×C5×C19
FrattiniC1G
Fitting, socleC2×C19×C31C3×C5
LCSG ▷ C31
UCSC1 ◁ C2×C19

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1178

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC4×C19×(C31⋊C3)⋊C5, C19×((C31⋊C3)⋊C4)⋊C5, Dic19×(C31⋊C3)⋊C5, …
maximal normal subgroup ofC4×C19×(C31⋊C3)⋊C5, C19×((C31⋊C3)⋊C4)⋊C5, Dic19×(C31⋊C3)⋊C5, …
maximal quotient ofC4×C19×(C31⋊C3)⋊C5, C22×C19×(C31⋊C3)⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17670, 7);