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C13⋊C3×(C5⋊D5)⋊C3 #19154349

order5850
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5

Aliases

direct productC13⋊C3×(C5⋊D5)⋊C3
unambiguous semidirect product(C13⋊C3×C5⋊D5)⋊C3
unambiguous semidirect product(C13×(C5⋊D5)⋊C3)⋊C3
unambiguous semidirect product((C5⋊D5)⋊(C13⋊C3))⋊C3

Splittings

Fitting, socle, derived, HallC52×C13 ⋊ C2×C32
HallC13⋊C3×C52⋊C3 ⋊ C2
HallC13×C5⋊D5 ⋊ C32
HallC5⋊D5 ⋊ C3×C13⋊C3
SylowC52 ⋊ C2×C3×C13⋊C3
SylowC13 ⋊ C3×(C5⋊D5)⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC52×C13C2×C32
LCSG ▷ C52×C13
UCSC1

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup of((C5⋊D5)⋊C3)⋊(D13⋊C3), C13⋊C3×#3874⋊C2, #16839083⋊C3, …
maximal normal subgroup of((C5⋊D5)⋊C3)⋊(D13⋊C3), C13⋊C3×#3874⋊C2, #16839083⋊C3, …
maximal quotient ofC13⋊C3×#1039⋊C3, C2×C13⋊C3×(C5⋊D5)⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5850, 65);