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C2×C3×C52×C13⋊C3 #19154381

order5850
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C2×C32×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC2×C3×C52×C13⋊C3
unambiguous semidirect product(C2×C13)⋊(C32×C52)
unambiguous semidirect product(C2×C3×C13)⋊(C3×C52)
unambiguous semidirect product(C2×C5×C13)⋊(C32×C5)
unambiguous semidirect product(C2×C3×C5×C13)⋊(C3×C5)

Splittings

Fitting, socleC2×C3×C52×C13 ⋊ C3
derived, SylowC13 ⋊ C2×C32×C52
HallC2×C52×C13 ⋊ C32
HallC52×C13 ⋊ C2×C32
HallC2×C13 ⋊ C32×C52

Subgroups

subgroupG/H
center, hypercenterC2×C3×C52C13⋊C3
commutator, hypocenterC13C2×C32×C52
FrattiniC1G
Fitting, socleC2×C3×C52×C13C3
LCSG ▷ C13
UCSC1 ◁ C2×C3×C52

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C52×Dic13⋊C3, C3×C5×Dic65⋊C3, C3×C5×Dic5×C13⋊C3, …
maximal normal subgroup ofC3×C52×Dic13⋊C3, C3×C5×Dic65⋊C3, C3×C5×Dic5×C13⋊C3, …
maximal quotient ofC3×C4×C52×C13⋊C3, C22×C3×C52×C13⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5850, 97);