Finite Group Databasebeta

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C4×C19×C41⋊C5 #29509977

order15580
isoclinismisoclinic class of C41⋊C5
automorphism?
homologyAbelianization (H1) = C4×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC4×C19×C41⋊C5
unambiguous semidirect product(C4×C41)⋊(C5×C19)
unambiguous semidirect product(C4×C19×C41)⋊C5

Splittings

Fitting, HallC4×C19×C41 ⋊ C5
derived, SylowC41 ⋊ C4×C5×C19
HallC19×C41 ⋊ C4×C5
HallC4×C41 ⋊ C5×C19

Subgroups

subgroupG/H
center, hypercenterC4×C19C41⋊C5
commutator, hypocenterC41C4×C5×C19
FrattiniC2C2×C19×C41⋊C5
FittingC4×C19×C41C5
socleC2×C19×C41C2×C5
prime radicalC2×C19×C41⋊C5C2
cosocleC2×C41C2×C5×C19
LCSG ▷ C41
UCSC1 ◁ C4×C19

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3116

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15580, 2);