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C3×C13⋊(D31⋊C5) #27130656

order12090
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13⋊(D31⋊C5)
unambiguous semidirect product(C3×D403)⋊C5

Splittings

Fitting, socle, HallC3×C13×C31 ⋊ C2×C5
derived, HallC13×C31 ⋊ C2×C3×C5
HallC3×C13×ΓL(1,𝔽32) ⋊ C2
HallC3×D403 ⋊ C5
HallC13×ΓL(1,𝔽32) ⋊ C2×C3
HallD403 ⋊ C3×C5
HallC3×ΓL(1,𝔽32) ⋊ D13
HallΓL(1,𝔽32) ⋊ C3×D13
HallC3×C31 ⋊ C5×D13
HallC3×C13 ⋊ D31⋊C5
SylowC31 ⋊ C3×C5×D13
SylowC13 ⋊ C3×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC3C13⋊(D31⋊C5)
commutator, cosocle, hypocenterC13×C31C2×C3×C5
FrattiniC1G
Fitting, socleC3×C13×C31C2×C5
LCSG ▷ C13×C31
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

237 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D13×D31⋊C5, D3×C13⋊(D31⋊C5), D39⋊(D31⋊C5), …
maximal normal subgroup ofC3×D13×D31⋊C5, D3×C13⋊(D31⋊C5), D39⋊(D31⋊C5), …
maximal quotient ofC3×ΓL(1,𝔽32)⋊Dic13, C2×C3×C13⋊(D31⋊C5), C9×C13⋊(D31⋊C5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12090, 28);