Finite Group Databasebeta

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C2×C11×C23×D21 #36318445

order21252
automorphism?
homologyAbelianization (H1) = C22×C11×C23 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×C23×D21
unambiguous semidirect product(C2×C3)⋊(C11×D7×C23)
unambiguous semidirect product(C2×C7)⋊(D3×C11×C23)

Splittings

Fitting, socleC2×C3×C7×C11×C23 ⋊ C2
derived, HallC3×C7 ⋊ C22×C11×C23
HallC3×C7×C11×C23 ⋊ C22
HallC7×C11×C23 ⋊ C2×D3
HallC3×C11×C23 ⋊ C2×D7
HallC3×C7×C23 ⋊ C22×C11
HallC3×C7×C11 ⋊ C22×C23
HallC7×C23 ⋊ C2×D3×C11
HallC7×C11 ⋊ C2×D3×C23
HallC3×C23 ⋊ C2×C11×D7
HallC3×C11 ⋊ C2×D7×C23
SylowC7 ⋊ C2×D3×C11×C23
SylowC3 ⋊ C2×C11×D7×C23

Subgroups

subgroupG/H
center, hypercenterC2×C11×C23D21
commutator, cosocle, hypocenterC3×C7C22×C11×C23
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C23C2
LCSG ▷ C3×C7
UCSC1 ◁ C2×C11×C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10626

Conjugacy classes & character table

6072 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21252, 123);