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C3×C5×C53⋊C13 #23780252

order10335
automorphism?
homologyAbelianization (H1) = C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C53⋊C13
unambiguous semidirect productC53⋊(C3×C5×C13)
unambiguous semidirect product(C3×C53)⋊(C5×C13)
unambiguous semidirect product(C5×C53)⋊(C3×C13)
unambiguous semidirect product(C3×C5×C53)⋊C13

Splittings

Fitting, socle, HallC3×C5×C53 ⋊ C13
derived, SylowC53 ⋊ C3×C5×C13
HallC5×C53 ⋊ C3×C13
HallC3×C53 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC3×C5C53⋊C13
commutator, cosocle, hypocenterC53C3×C5×C13
FrattiniC1G
Fitting, socleC3×C5×C53C13
LCSG ▷ C53
UCSC1 ◁ C3×C5

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C3×C5×C53⋊C13, C3×C5×D53⋊C13, C3×D5×C53⋊C13, …
maximal normal subgroup ofC2×C3×C5×C53⋊C13, C3×C5×D53⋊C13, C3×D5×C53⋊C13, …
maximal quotient ofC2×C3×C5×C53⋊C13, C5×C9×C53⋊C13, C32×C5×C53⋊C13

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10335, 2);