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C5×C13⋊C3×D41 #30630539

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

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5C13⋊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

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

Relationships

maximal subgroup ofC5×#14523824⋊C3, C5×D13⋊C3×D41, C5×C13⋊C3×#4223, …
maximal normal subgroup ofC5×#14523824⋊C3, C5×D13⋊C3×D41, C5×C13⋊C3×#4223, …
maximal quotient ofC5×C13⋊C3×Dic41, C2×C5×C13⋊C3×D41

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15990, 27);