Finite Group Databasebeta

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C2×C19×D71⋊C5 #41008688

order26980
automorphism?
homologyAbelianization (H1) = C22×C5×C19 · Schur multiplier (H2) = C2

Aliases

direct productC2×C19×D71⋊C5
unambiguous semidirect productD71⋊(C2×C5×C19)
unambiguous semidirect product(C2×D71)⋊(C5×C19)
unambiguous semidirect product(C71⋊C5)⋊(C22×C19)
unambiguous semidirect product(C2×C71⋊C5)⋊(C2×C19)
unambiguous semidirect product(C2×C19×D71)⋊C5

Splittings

Fitting, socleC2×C19×C71 ⋊ C2×C5
derived, SylowC71 ⋊ C22×C5×C19
HallC19×C71⋊C5 ⋊ C22
HallC2×C19×D71 ⋊ C5
HallC19×C71 ⋊ C22×C5
HallC71⋊C5 ⋊ C22×C19
HallC2×D71 ⋊ C5×C19

Subgroups

subgroupG/H
center, hypercenterC2×C19D71⋊C5
commutator, cosocle, hypocenterC71C22×C5×C19
FrattiniC1G
Fitting, socleC2×C19×C71C2×C5
LCSG ▷ C71
UCSC1 ◁ C2×C19

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2698

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26980, 15);