Finite Group Databasebeta

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C2×C29×D41⋊C5 #37558068

order23780
automorphism?
homologyAbelianization (H1) = C22×C5×C29 · Schur multiplier (H2) = C2

Aliases

direct productC2×C29×D41⋊C5
unambiguous semidirect productD41⋊(C2×C5×C29)
unambiguous semidirect product(C2×D41)⋊(C5×C29)
unambiguous semidirect product(C41⋊C5)⋊(C22×C29)
unambiguous semidirect product(C2×C41⋊C5)⋊(C2×C29)
unambiguous semidirect product(C2×C29×D41)⋊C5

Splittings

Fitting, socleC2×C29×C41 ⋊ C2×C5
derived, SylowC41 ⋊ C22×C5×C29
HallC29×C41⋊C5 ⋊ C22
HallC2×C29×D41 ⋊ C5
HallC29×C41 ⋊ C22×C5
HallC41⋊C5 ⋊ C22×C29
HallC2×D41 ⋊ C5×C29

Subgroups

subgroupG/H
center, hypercenterC2×C29D41⋊C5
commutator, cosocle, hypocenterC41C22×C5×C29
FrattiniC1G
Fitting, socleC2×C29×C41C2×C5
LCSG ▷ C41
UCSC1 ◁ C2×C29

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2378

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23780, 21);