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C19×(C31⋊C3)⋊C5 #22579550

order8835
isoclinismisoclinic class of (C31⋊C3)⋊C5
automorphism?
homologyAbelianization (H1) = C3×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×(C31⋊C3)⋊C5
unambiguous semidirect product(C31⋊C3)⋊(C5×C19)
unambiguous semidirect productΓL(1,𝔽32)⋊(C3×C19)
unambiguous semidirect product(C19×C31⋊C3)⋊C5

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC19(C31⋊C3)⋊C5
commutator, hypocenterC31C3×C5×C19
FrattiniC1G
Fitting, socleC19×C31C3×C5
LCSG ▷ C31
UCSC1 ◁ C19

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

323 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C19×(C31⋊C3)⋊C5, C19×AGL(1,𝔽31), D19×(C31⋊C3)⋊C5, …
maximal normal subgroup ofC2×C19×(C31⋊C3)⋊C5, C19×AGL(1,𝔽31), D19×(C31⋊C3)⋊C5, …
maximal quotient ofC2×C19×(C31⋊C3)⋊C5, C19×ΓL(1,𝔽32)⋊C9, C3×C19×(C31⋊C3)⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8835, 7);