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C2×C3×C7⋊AGL(1,𝔽23) #36318375

order21252
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7⋊AGL(1,𝔽23)
unambiguous semidirect product(C2×C23⋊C11)⋊(C3×D7)
unambiguous semidirect product(C2×C3×D161)⋊C11

Splittings

Fitting, socleC2×C3×C7×C23 ⋊ C2×C11
derived, HallC7×C23 ⋊ C22×C3×C11
HallC3×C7×C23⋊C11 ⋊ C22
HallC2×C3×D161 ⋊ C11
HallC7×C23⋊C11 ⋊ C22×C3
HallC3×C23⋊C11 ⋊ C2×D7
HallC2×D161 ⋊ C3×C11
HallC3×C7×C23 ⋊ C22×C11
HallC23⋊C11 ⋊ C2×C3×D7
HallC3×C23 ⋊ C2×C11×D7
SylowC23 ⋊ C2×C3×C11×D7
HallC3×C7 ⋊ C2×AGL(1,𝔽23)
SylowC7 ⋊ C2×C3×AGL(1,𝔽23)

Subgroups

subgroupG/H
center, hypercenterC2×C3C7⋊AGL(1,𝔽23)
commutator, cosocle, hypocenterC7×C23C22×C3×C11
FrattiniC1G
Fitting, socleC2×C3×C7×C23C2×C11
LCSG ▷ C7×C23
UCSC1 ◁ C2×C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 966

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21252, 53);