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D3×C5⋊(D31⋊C5) #22604837

order9300
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productD3×C5⋊(D31⋊C5)
unambiguous semidirect product(C5×D3)⋊(D31⋊C5)
unambiguous semidirect product(D3×ΓL(1,𝔽32))⋊D5
unambiguous semidirect product(D3×D155)⋊C5

Splittings

Fitting, socle, derivedC3×C5×C31 ⋊ C22×C5
HallC3×C5×ΓL(1,𝔽32) ⋊ C22
HallC5×ΓL(1,𝔽32) ⋊ C2×D3
HallC3×C31 ⋊ C2×C5×D5
SylowC31 ⋊ C5×D3×D5
SylowC3 ⋊ C2×C5⋊(D31⋊C5)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C31C22×C5
LCSG ▷ C3×C5×C31
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

105 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD9×C5⋊(D31⋊C5), D3×C5⋊AGL(1,𝔽31), C3×D3×C5⋊(D31⋊C5), …
maximal normal subgroup ofD3×C5⋊AGL(1,𝔽31), C3×D3×C5⋊(D31⋊C5)
maximal quotient ofD9×C5⋊(D31⋊C5), C3×D3×C5⋊(D31⋊C5), D3×C3⋊(C5⋊(D31⋊C5)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9300, 111);