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C13×C5⋊(D61⋊C3) #37558204

order23790
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C5⋊(D61⋊C3)
unambiguous semidirect productC5⋊(C13×D61⋊C3)
unambiguous semidirect product(C61⋊C3)⋊(D5×C13)
unambiguous semidirect productD305⋊(C3×C13)

Splittings

Fitting, socle, HallC5×C13×C61 ⋊ C2×C3
derived, HallC5×C61 ⋊ C2×C3×C13
HallC5×C13×C61⋊C3 ⋊ C2
HallC13×D305 ⋊ C3
HallC13×C61⋊C3 ⋊ D5
HallC5×C61⋊C3 ⋊ C2×C13
HallC13×C61 ⋊ C3×D5
HallD305 ⋊ C3×C13
HallC61⋊C3 ⋊ D5×C13
HallC5×C13 ⋊ D61⋊C3
SylowC61 ⋊ C3×D5×C13
SylowC5 ⋊ C13×D61⋊C3

Subgroups

subgroupG/H
center, hypercenterC13C5⋊(D61⋊C3)
commutator, cosocle, hypocenterC5×C61C2×C3×C13
FrattiniC1G
Fitting, socleC5×C13×C61C2×C3
LCSG ▷ C5×C61
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3965

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23790, 49);