Finite Group Databasebeta

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D3×C7×C23⋊C11 #24922315

order10626
automorphism?
homologyAbelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productD3×C7×C23⋊C11
unambiguous semidirect productC3⋊(C2×C7×C23⋊C11)
unambiguous semidirect product(D3×C23)⋊(C7×C11)
unambiguous semidirect product(D3×C7×C23)⋊C11

Splittings

Fitting, socle, HallC3×C7×C23 ⋊ C2×C11
derived, HallC3×C23 ⋊ C2×C7×C11
HallC3×C7×C23⋊C11 ⋊ C2
HallD3×C7×C23 ⋊ C11
HallC3×C23⋊C11 ⋊ C2×C7
HallC7×C23 ⋊ D3×C11
HallD3×C23 ⋊ C7×C11
SylowC23 ⋊ D3×C7×C11
HallC3×C7 ⋊ C2×C23⋊C11
SylowC3 ⋊ C2×C7×C23⋊C11

Subgroups

subgroupG/H
center, hypercenterC7D3×C23⋊C11
commutator, cosocle, hypocenterC3×C23C2×C7×C11
FrattiniC1G
Fitting, socleC3×C7×C23C2×C11
LCSG ▷ C3×C23
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

273 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C7×AGL(1,𝔽23), D3×C7⋊AGL(1,𝔽23), D3×D7×C23⋊C11, …
maximal normal subgroup ofD3×C7×AGL(1,𝔽23), D3×C7⋊AGL(1,𝔽23), D3×D7×C23⋊C11, …
maximal quotient ofC7×Dic3×C23⋊C11, C2×D3×C7×C23⋊C11, C7×D9×C23⋊C11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10626, 23);