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D3×#13133721 #23779451

order10230
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productD3×#13133721
unambiguous semidirect productC3⋊(C2×#13133721)

Splittings

Fitting, socle, derived, HallC3×C11×C31 ⋊ C2×C5
HallC3×#13133721 ⋊ C2
HallD3×C11×C31 ⋊ C5
HallC11×C31 ⋊ C5×D3
HallD3×C31 ⋊ C11⋊C5
HallC3×C31 ⋊ C2×C11⋊C5
HallD3×C11 ⋊ ΓL(1,𝔽32)
HallC3×C11 ⋊ C2×ΓL(1,𝔽32)
SylowC31 ⋊ D3×C11⋊C5
SylowC11 ⋊ D3×ΓL(1,𝔽32)
SylowC3 ⋊ C2×#13133721

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C31C2×C5
LCSG ▷ C3×C11×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

219 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×#16811783, D3×#16811777, D3×#16811771, …
maximal normal subgroup ofD3×#16811783, D3×#16811777, D3×#16811771, …
maximal quotient ofDic3×#13133721, C2×D3×#13133721, D9×#13133721, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10230, 50);