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C5×C13×D37⋊C3 #28385804

order14430
isoclinismisoclinic class of D37⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13×D37⋊C3
unambiguous semidirect productD37⋊(C3×C5×C13)
unambiguous semidirect product(C37⋊C3)⋊(C2×C5×C13)
unambiguous semidirect product(C5×D37)⋊(C3×C13)

Splittings

Fitting, socle, HallC5×C13×C37 ⋊ C2×C3
derived, SylowC37 ⋊ C2×C3×C5×C13
HallC5×C13×C37⋊C3 ⋊ C2
HallC5×C13×D37 ⋊ C3
HallC13×C37⋊C3 ⋊ C2×C5
HallC13×D37 ⋊ C3×C5
HallC5×C37⋊C3 ⋊ C2×C13
HallC13×C37 ⋊ C2×C3×C5
HallC5×D37 ⋊ C3×C13
HallC5×C37 ⋊ C2×C3×C13
HallC37⋊C3 ⋊ C2×C5×C13
HallD37 ⋊ C3×C5×C13

Subgroups

subgroupG/H
center, hypercenterC5×C13D37⋊C3
commutator, cosocle, hypocenterC37C2×C3×C5×C13
FrattiniC1G
Fitting, socleC5×C13×C37C2×C3
LCSG ▷ C37
UCSC1 ◁ C5×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2405

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×C13×#3866⋊C3, C5×#19153517, C5×D13×D37⋊C3, …
maximal normal subgroup ofC5×C13×#3866⋊C3, C5×#19153517, C5×D13×D37⋊C3, …
maximal quotient ofC5×C13×Dic37⋊C3, C2×C5×C13×D37⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14430, 21);