Finite Group Databasebeta

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C4×C19×C71⋊C5 #41008675

order26980
automorphism?
homologyAbelianization (H1) = C4×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC4×C19×C71⋊C5
unambiguous semidirect product(C4×C71)⋊(C5×C19)
unambiguous semidirect product(C4×C19×C71)⋊C5

Splittings

Fitting, HallC4×C19×C71 ⋊ C5
derived, SylowC71 ⋊ C4×C5×C19
HallC19×C71 ⋊ C4×C5
HallC4×C71 ⋊ C5×C19

Subgroups

subgroupG/H
center, hypercenterC4×C19C71⋊C5
commutator, hypocenterC71C4×C5×C19
FrattiniC2C2×C19×C71⋊C5
FittingC4×C19×C71C5
socleC2×C19×C71C2×C5
prime radicalC2×C19×C71⋊C5C2
cosocleC2×C71C2×C5×C19
LCSG ▷ C71
UCSC1 ◁ C4×C19

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5396

Conjugacy classes & character table

1444 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26980, 2);