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C13×C3⋊(D61⋊C5) #37558185

order23790
automorphism?
homologyAbelianization (H1) = C2×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C3⋊(D61⋊C5)
unambiguous semidirect productC3⋊(C13×D61⋊C5)
unambiguous semidirect product(C61⋊C5)⋊(D3×C13)
unambiguous semidirect productD183⋊(C5×C13)
unambiguous semidirect product(C13×D183)⋊C5

Splittings

Fitting, socle, HallC3×C13×C61 ⋊ C2×C5
derived, HallC3×C61 ⋊ C2×C5×C13
HallC3×C13×C61⋊C5 ⋊ C2
HallC13×D183 ⋊ C5
HallC13×C61⋊C5 ⋊ D3
HallC3×C61⋊C5 ⋊ C2×C13
HallC13×C61 ⋊ C5×D3
HallD183 ⋊ C5×C13
HallC61⋊C5 ⋊ D3×C13
SylowC61 ⋊ C5×D3×C13
HallC3×C13 ⋊ D61⋊C5
SylowC3 ⋊ C13×D61⋊C5

Subgroups

subgroupG/H
center, hypercenterC13C3⋊(D61⋊C5)
commutator, cosocle, hypocenterC3×C61C2×C5×C13
FrattiniC1G
Fitting, socleC3×C13×C61C2×C5
LCSG ▷ C3×C61
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2379

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23790, 30);