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C13⋊C3×D41⋊C5 #30630546

order15990
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC13⋊C3×D41⋊C5
unambiguous semidirect productD41⋊(C5×C13⋊C3)
unambiguous semidirect product(C41⋊C5)⋊(C2×C13⋊C3)
unambiguous semidirect product(C13⋊C3×D41)⋊C5
unambiguous semidirect product(C13×D41⋊C5)⋊C3

Splittings

Fitting, socle, derived, HallC13×C41 ⋊ C2×C3×C5
HallC13⋊C3×C41⋊C5 ⋊ C2
HallC13×D41⋊C5 ⋊ C3
HallC13⋊C3×D41 ⋊ C5
HallC13×C41⋊C5 ⋊ C2×C3
HallC13⋊C3×C41 ⋊ C2×C5
HallC13×D41 ⋊ C3×C5
HallC41⋊C5 ⋊ C2×C13⋊C3
HallD41 ⋊ C5×C13⋊C3
SylowC41 ⋊ C2×C5×C13⋊C3
SylowC13 ⋊ C3×D41⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C41C2×C3×C5
LCSG ▷ C13×C41
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 533

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(#14523824⋊C3)⋊C5, D13⋊C3×D41⋊C5, C13⋊C3×#4223⋊C5, …
maximal normal subgroup of(#14523824⋊C3)⋊C5, D13⋊C3×D41⋊C5, C13⋊C3×#4223⋊C5, …
maximal quotient ofC13⋊C3×Dic41⋊C5, C2×C13⋊C3×D41⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15990, 34);