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C3×Dic5×C13⋊C3 #14556751

order2340
isoclinismisoclinic class of D5×C13⋊C3
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×Dic5×C13⋊C3
unambiguous semidirect product(C13×Dic5)⋊C32
unambiguous semidirect product(C3×C13×Dic5)⋊C3

Splittings

derived, HallC5×C13 ⋊ C32×C4
HallC3×C5×C13⋊C3 ⋊ C4
HallC13×Dic5 ⋊ C32
SylowC13 ⋊ C32×Dic5
SylowC5 ⋊ C3×C4×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3D5×C13⋊C3
commutator, hypocenterC5×C13C32×C4
FrattiniC2C3×D5×C13⋊C3
Fitting, socleC2×C3×C5×C13C2×C3
prime radicalC2×C3×C5×C13⋊C3C2
cosocleC2×C5×C13C2×C32
LCSG ▷ C5×C13
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 780

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C13⋊C3×Dic25, C3×C5×Dic5×C13⋊C3, C3×C13⋊C3×#1039, …
maximal normal subgroup ofC3×C5×Dic5×C13⋊C3, C3×C7×Dic5×C13⋊C3, C3×C11×Dic5×C13⋊C3, …
maximal quotient ofC3×C13⋊C3×Dic25, C3×C5×Dic5×C13⋊C3, C3×C13⋊C3×#1039, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2340, 55);