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C61×C5⋊(D13⋊C3) #37558209

order23790
automorphism?
homologyAbelianization (H1) = C2×C3×C61 · Schur multiplier (H2) = C1

Aliases

direct productC61×C5⋊(D13⋊C3)
unambiguous semidirect productC5⋊(C61×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(D5×C61)
unambiguous semidirect productD65⋊(C3×C61)

Splittings

Fitting, socle, HallC5×C13×C61 ⋊ C2×C3
derived, HallC5×C13 ⋊ C2×C3×C61
HallC5×C13⋊C3×C61 ⋊ C2
HallC61×D65 ⋊ C3
HallC13⋊C3×C61 ⋊ D5
HallC13×C61 ⋊ C3×D5
HallC5×C61 ⋊ D13⋊C3
HallC5×C13⋊C3 ⋊ C2×C61
HallD65 ⋊ C3×C61
HallC13⋊C3 ⋊ D5×C61
SylowC13 ⋊ C3×D5×C61
SylowC5 ⋊ C61×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC61C5⋊(D13⋊C3)
commutator, cosocle, hypocenterC5×C13C2×C3×C61
FrattiniC1G
Fitting, socleC5×C13×C61C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C61

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3965

Conjugacy classes & character table

1342 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23790, 54);