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C3×C13×(C5⋊D5)⋊C3 #19154359

order5850
isoclinismisoclinic class of (C5⋊D5)⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32×C13 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×C13×(C5⋊D5)⋊C3
unambiguous semidirect product(C5⋊D5)⋊(C32×C13)
unambiguous semidirect product(C3×C5⋊D5)⋊(C3×C13)

Splittings

Fitting, socleC3×C52×C13 ⋊ C2×C3
derived, SylowC52 ⋊ C2×C32×C13
HallC3×C13×C52⋊C3 ⋊ C2
HallC13×C5⋊D5 ⋊ C32
HallC52×C13 ⋊ C2×C32
HallC3×C52⋊C3 ⋊ C2×C13
HallC5⋊D5 ⋊ C32×C13

Subgroups

subgroupG/H
center, hypercenterC3×C13(C5⋊D5)⋊C3
commutator, hypocenterC52C2×C32×C13
FrattiniC1G
Fitting, socleC3×C52×C13C2×C3
LCSG ▷ C52
UCSC1 ◁ C3×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

390 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C13×#3874⋊C2, C3×((C5⋊D5)⋊C3)⋊D13, C3×C13×#1043⋊C3, …
maximal normal subgroup ofC3×C13×#3874⋊C2, C3×((C5⋊D5)⋊C3)⋊D13, C3×C13×#1043⋊C3, …
maximal quotient ofC3×C13×#1039⋊C3, C2×C3×C13×(C5⋊D5)⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5850, 75);