Finite Group Databasebeta

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C3×D5×C13×C41 #30630520

order15990
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C3×C13×C41 · Schur multiplier (H2) = C1

Aliases

direct productC3×D5×C13×C41
unambiguous semidirect productC5⋊(C2×C3×C13×C41)

Splittings

Fitting, socle, HallC3×C5×C13×C41 ⋊ C2
derived, SylowC5 ⋊ C2×C3×C13×C41
HallC5×C13×C41 ⋊ C2×C3
HallC3×C5×C41 ⋊ C2×C13
HallC5×C41 ⋊ C2×C3×C13
HallC3×C5×C13 ⋊ C2×C41
HallC5×C13 ⋊ C2×C3×C41
HallC3×C5 ⋊ C2×C13×C41

Subgroups

subgroupG/H
center, hypercenterC3×C13×C41D5
commutator, cosocle, hypocenterC5C2×C3×C13×C41
FrattiniC1G
Fitting, socleC3×C5×C13×C41C2
LCSG ▷ C5
UCSC1 ◁ C3×C13×C41

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

6396 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C13×AGL(1,𝔽5)×C41, C3×C13×#11717963, C3×C41×#63120, …
maximal normal subgroup ofC3×C13×AGL(1,𝔽5)×C41, C3×C13×#11717963, C3×C41×#63120, …
maximal quotient ofC3×C13×Dic5×C41, C2×C3×D5×C13×C41

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15990, 8);