Finite Group Databasebeta

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D3×C7×C11×C23 #24922304

order10626
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C2×C7×C11×C23 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC3×C7×C11×C23 ⋊ C2
derived, SylowC3 ⋊ C2×C7×C11×C23
HallC3×C11×C23 ⋊ C2×C7
HallC3×C7×C23 ⋊ C2×C11
HallC3×C7×C11 ⋊ C2×C23
HallC3×C23 ⋊ C2×C7×C11
HallC3×C11 ⋊ C2×C7×C23
HallC3×C7 ⋊ C2×C11×C23

Subgroups

subgroupG/H
center, hypercenterC7×C11×C23D3
commutator, cosocle, hypocenterC3C2×C7×C11×C23
FrattiniC1G
Fitting, socleC3×C7×C11×C23C2
LCSG ▷ C3
UCSC1 ◁ C7×C11×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5313 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C7×C11×D23, D3×C7×D11×C23, D3×C7×D253, …
maximal normal subgroup ofD3×C7×C11×D23, D3×C7×D11×C23, D3×C7×D253, …
maximal quotient ofC7×C11×Dic3×C23, C2×D3×C7×C11×C23, C7×C11×D9×C23, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10626, 12);