Finite Group Databasebeta

← Prev (#36318435) Next (#36318437) →

C2×C3×C7×D253 #36318436

order21252
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7×D253
unambiguous semidirect product(C2×C11)⋊(C3×C7×D23)
unambiguous semidirect product(C2×C23)⋊(C3×C7×D11)

Splittings

Fitting, socleC2×C3×C7×C11×C23 ⋊ C2
derived, HallC11×C23 ⋊ C22×C3×C7
HallC3×C7×C11×C23 ⋊ C22
HallC7×C11×C23 ⋊ C22×C3
HallC3×C11×C23 ⋊ C22×C7
HallC3×C7×C23 ⋊ C2×D11
HallC3×C7×C11 ⋊ C2×D23
HallC7×C23 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×D23
HallC3×C23 ⋊ C2×C7×D11
HallC3×C11 ⋊ C2×C7×D23
SylowC23 ⋊ C2×C3×C7×D11
SylowC11 ⋊ C2×C3×C7×D23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D253
commutator, cosocle, hypocenterC11×C23C22×C3×C7
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C23C2
LCSG ▷ C11×C23
UCSC1 ◁ C2×C3×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10626

Conjugacy classes & character table

5376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21252, 114);