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D13×(C61⋊C3)⋊C5 #37558220

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

Aliases

direct productD13×(C61⋊C3)⋊C5
unambiguous semidirect product(D13×C61⋊C3)⋊C5

Splittings

Fitting, socle, derived, HallC13×C61 ⋊ C2×C3×C5
HallC13×(C61⋊C3)⋊C5 ⋊ C2
HallD13×C61⋊C5 ⋊ C3
HallD13×C61⋊C3 ⋊ C5
HallC13×C61⋊C5 ⋊ C2×C3
HallC13×C61⋊C3 ⋊ C2×C5
HallD13×C61 ⋊ C3×C5
HallC61⋊C5 ⋊ C3×D13
HallC61⋊C3 ⋊ C5×D13
SylowC61 ⋊ C3×C5×D13
SylowC13 ⋊ C2×(C61⋊C3)⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C61C2×C3×C5
LCSG ▷ C13×C61
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 793

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23790, 65);