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C5×C7×C3⋊(D13⋊C3) #22551252

order8190
isoclinismisoclinic class of C3⋊(D13⋊C3)
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×C3⋊(D13⋊C3)
unambiguous semidirect productC3⋊(C5×C7×D13⋊C3)
unambiguous semidirect product(C13⋊C3)⋊(C5×D3×C7)
unambiguous semidirect productD39⋊(C3×C5×C7)
unambiguous semidirect product(C5×D39)⋊(C3×C7)

Splittings

Fitting, socleC3×C5×C7×C13 ⋊ C2×C3
derivedC3×C13 ⋊ C2×C3×C5×C7
HallC3×C5×C7×C13⋊C3 ⋊ C2
HallC3×C7×C13⋊C3 ⋊ C2×C5
HallC3×C5×C13⋊C3 ⋊ C2×C7
HallC5×C7×C13 ⋊ C3×D3
HallC3×C13⋊C3 ⋊ C2×C5×C7
HallC7×C13 ⋊ C3×C5×D3
HallC5×C13 ⋊ C3×D3×C7
SylowC13 ⋊ C3×C5×D3×C7

Subgroups

subgroupG/H
center, hypercenterC5×C7C3⋊(D13⋊C3)
commutator, hypocenterC3×C13C2×C3×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C13C2×C3
LCSG ▷ C3×C13
UCSC1 ◁ C5×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

525 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D3×C7×D13⋊C3, C5×D7×C3⋊(D13⋊C3), C5×(C3⋊(D13⋊C3))⋊D7, …
maximal normal subgroup ofC5×D3×C7×D13⋊C3, C5×D7×C3⋊(D13⋊C3), C5×(C3⋊(D13⋊C3))⋊D7, …
maximal quotient ofC5×C7×C3⋊(Dic13⋊C3), C2×C5×C7×C3⋊(D13⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8190, 86);