Finite Group Databasebeta

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C2×C43×D31⋊C5 #40998621

order26660
automorphism?
homologyAbelianization (H1) = C22×C5×C43 · Schur multiplier (H2) = C2

Aliases

direct productC2×C43×D31⋊C5
unambiguous semidirect productD31⋊(C2×C5×C43)
unambiguous semidirect product(C2×D31)⋊(C5×C43)
unambiguous semidirect productΓL(1,𝔽32)⋊(C22×C43)
unambiguous semidirect product(C2×ΓL(1,𝔽32))⋊(C2×C43)
unambiguous semidirect product(C2×C43×D31)⋊C5

Splittings

Fitting, socleC2×C31×C43 ⋊ C2×C5
derived, SylowC31 ⋊ C22×C5×C43
HallC43×ΓL(1,𝔽32) ⋊ C22
HallC2×C43×D31 ⋊ C5
HallC31×C43 ⋊ C22×C5
HallΓL(1,𝔽32) ⋊ C22×C43
HallC2×D31 ⋊ C5×C43

Subgroups

subgroupG/H
center, hypercenterC2×C43D31⋊C5
commutator, cosocle, hypocenterC31C22×C5×C43
FrattiniC1G
Fitting, socleC2×C31×C43C2×C5
LCSG ▷ C31
UCSC1 ◁ C2×C43

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2666

Conjugacy classes & character table

1118 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26660, 15);