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C5×(C13⋊C3)⋊D61 #37558197

order23790
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C13⋊C3)⋊D61
unambiguous semidirect product(C13⋊C3)⋊(C5×D61)

Splittings

Fitting, socle, HallC5×C13×C61 ⋊ C2×C3
derived, HallC13×C61 ⋊ C2×C3×C5
HallC5×C13⋊C3×C61 ⋊ C2
HallC5×D793 ⋊ C3
HallC13⋊C3×C61 ⋊ C2×C5
HallD793 ⋊ C3×C5
HallC5×C61 ⋊ D13⋊C3
HallC5×C13⋊C3 ⋊ D61
HallC5×C13 ⋊ C3×D61
SylowC61 ⋊ C5×D13⋊C3
HallC13⋊C3 ⋊ C5×D61
SylowC13 ⋊ C3×C5×D61

Subgroups

subgroupG/H
center, hypercenterC5(C13⋊C3)⋊D61
commutator, cosocle, hypocenterC13×C61C2×C3×C5
FrattiniC1G
Fitting, socleC5×C13×C61C2×C3
LCSG ▷ C13×C61
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3965

Conjugacy classes & character table

1090 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23790, 42);