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C5×C13⋊C3×C53 #23780253

order10335
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C3×C5×C53 · Schur multiplier (H2) = C1

Aliases

direct productC5×C13⋊C3×C53
unambiguous semidirect productC13⋊(C3×C5×C53)
unambiguous semidirect product(C5×C13)⋊(C3×C53)
unambiguous semidirect product(C13×C53)⋊(C3×C5)
unambiguous semidirect product(C5×C13×C53)⋊C3

Splittings

Fitting, socle, HallC5×C13×C53 ⋊ C3
derived, SylowC13 ⋊ C3×C5×C53
HallC13×C53 ⋊ C3×C5
HallC5×C13 ⋊ C3×C53

Subgroups

subgroupG/H
center, hypercenterC5×C53C13⋊C3
commutator, cosocle, hypocenterC13C3×C5×C53
FrattiniC1G
Fitting, socleC5×C13×C53C3
LCSG ▷ C13
UCSC1 ◁ C5×C53

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1855 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C13⋊C3×C53, C5×C13⋊C3×D53, C5×C53×D13⋊C3, …
maximal normal subgroup ofC2×C5×C13⋊C3×C53, C5×C13⋊C3×D53, C5×C53×D13⋊C3, …
maximal quotient ofC2×C5×C13⋊C3×C53, C5×C53×C13⋊C9, C3×C5×C13⋊C3×C53

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10335, 3);