Finite Group Databasebeta

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C2×C13×D61⋊C5 #30629427

order15860
automorphism?
homologyAbelianization (H1) = C22×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×D61⋊C5
unambiguous semidirect productD61⋊(C2×C5×C13)
unambiguous semidirect product(C2×D61)⋊(C5×C13)
unambiguous semidirect product(C61⋊C5)⋊(C22×C13)
unambiguous semidirect product(C2×C61⋊C5)⋊(C2×C13)
unambiguous semidirect product(C2×C13×D61)⋊C5

Splittings

Fitting, socleC2×C13×C61 ⋊ C2×C5
derived, SylowC61 ⋊ C22×C5×C13
HallC13×C61⋊C5 ⋊ C22
HallC2×C13×D61 ⋊ C5
HallC13×C61 ⋊ C22×C5
HallC61⋊C5 ⋊ C22×C13
HallC2×D61 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13D61⋊C5
commutator, cosocle, hypocenterC61C22×C5×C13
FrattiniC1G
Fitting, socleC2×C13×C61C2×C5
LCSG ▷ C61
UCSC1 ◁ C2×C13

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1586

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15860, 21);