Finite Group Databasebeta

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D39×C61⋊C5 #37558186

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

Aliases

direct productD39×C61⋊C5
unambiguous semidirect productC3⋊(D13×C61⋊C5)
unambiguous semidirect productC13⋊(D3×C61⋊C5)
unambiguous semidirect product(C61×D39)⋊C5

Splittings

Fitting, socle, derived, HallC3×C13×C61 ⋊ C2×C5
HallC3×C13×C61⋊C5 ⋊ C2
HallC61×D39 ⋊ C5
HallC13×C61⋊C5 ⋊ D3
HallC3×C61⋊C5 ⋊ D13
HallC13×C61 ⋊ C5×D3
HallC3×C61 ⋊ C5×D13
SylowC61 ⋊ C5×D39
HallC3×C13 ⋊ C2×C61⋊C5
SylowC13 ⋊ D3×C61⋊C5
SylowC3 ⋊ D13×C61⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C13×C61C2×C5
LCSG ▷ C3×C13×C61
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2379

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23790, 31);