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C5×C41×D13⋊C3 #30630540

order15990
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C41 · Schur multiplier (H2) = C1

Aliases

direct productC5×C41×D13⋊C3
unambiguous semidirect productD13⋊(C3×C5×C41)
unambiguous semidirect product(C13⋊C3)⋊(C2×C5×C41)
unambiguous semidirect product(C5×D13)⋊(C3×C41)
unambiguous semidirect product(C5×D13×C41)⋊C3

Splittings

Fitting, socle, HallC5×C13×C41 ⋊ C2×C3
derived, SylowC13 ⋊ C2×C3×C5×C41
HallC5×C13⋊C3×C41 ⋊ C2
HallC5×D13×C41 ⋊ C3
HallC13⋊C3×C41 ⋊ C2×C5
HallD13×C41 ⋊ C3×C5
HallC13×C41 ⋊ C2×C3×C5
HallC5×C13⋊C3 ⋊ C2×C41
HallC5×D13 ⋊ C3×C41
HallC5×C13 ⋊ C2×C3×C41
HallC13⋊C3 ⋊ C2×C5×C41
HallD13 ⋊ C3×C5×C41

Subgroups

subgroupG/H
center, hypercenterC5×C41D13⋊C3
commutator, cosocle, hypocenterC13C2×C3×C5×C41
FrattiniC1G
Fitting, socleC5×C13×C41C2×C3
LCSG ▷ C13
UCSC1 ◁ C5×C41

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2665

Conjugacy classes & character table

1640 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C41×AGL(1,𝔽13), C5×#14523823⋊C3, C5×D13⋊C3×D41, …
maximal normal subgroup ofC5×C41×AGL(1,𝔽13), C5×#14523823⋊C3, C5×D13⋊C3×D41, …
maximal quotient ofC5×C41×Dic13⋊C3, C2×C5×C41×D13⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15990, 28);