Finite Group Databasebeta

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C2×D3×C7×C11×C23 #36318441

order21252
automorphism?
homologyAbelianization (H1) = C22×C7×C11×C23 · Schur multiplier (H2) = C2

Aliases

direct productC2×D3×C7×C11×C23
unambiguous semidirect productC3⋊(C22×C7×C11×C23)
unambiguous semidirect product(C2×C3)⋊(C2×C7×C11×C23)

Splittings

Fitting, socleC2×C3×C7×C11×C23 ⋊ C2
derived, SylowC3 ⋊ C22×C7×C11×C23
HallC3×C7×C11×C23 ⋊ C22
HallC3×C11×C23 ⋊ C22×C7
HallC3×C7×C23 ⋊ C22×C11
HallC3×C7×C11 ⋊ C22×C23
HallC3×C23 ⋊ C22×C7×C11
HallC3×C11 ⋊ C22×C7×C23
HallC3×C7 ⋊ C22×C11×C23

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11×C23D3
commutator, cosocle, hypocenterC3C22×C7×C11×C23
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C23C2
LCSG ▷ C3
UCSC1 ◁ C2×C7×C11×C23

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10626

Conjugacy classes & character table

10626 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21252, 119);