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C5×(C13⋊C3)⋊D41 #30630541

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

Aliases

direct productC5×(C13⋊C3)⋊D41
unambiguous semidirect product(C13⋊C3)⋊(C5×D41)
unambiguous semidirect product(C5×D533)⋊C3

Splittings

Fitting, socle, HallC5×C13×C41 ⋊ C2×C3
derived, HallC13×C41 ⋊ C2×C3×C5
HallC5×C13⋊C3×C41 ⋊ C2
HallC5×D533 ⋊ C3
HallC13⋊C3×C41 ⋊ C2×C5
HallD533 ⋊ C3×C5
HallC5×C41 ⋊ D13⋊C3
HallC5×C13⋊C3 ⋊ D41
HallC5×C13 ⋊ C3×D41
SylowC41 ⋊ C5×D13⋊C3
HallC13⋊C3 ⋊ C5×D41
SylowC13 ⋊ C3×C5×D41

Subgroups

subgroupG/H
center, hypercenterC5(C13⋊C3)⋊D41
commutator, cosocle, hypocenterC13×C41C2×C3×C5
FrattiniC1G
Fitting, socleC5×C13×C41C2×C3
LCSG ▷ C13×C41
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2665

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×#14523821⋊C3, C5×#14523822⋊C3, C5×D13⋊C3×D41, …
maximal normal subgroup ofC5×#14523821⋊C3, C5×#14523822⋊C3, C5×D13⋊C3×D41, …
maximal quotient ofC5×Dic533⋊C3, C2×C5×(C13⋊C3)⋊D41

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15990, 29);