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D21×AGL(1,𝔽23) #36318366

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

Aliases

direct productD21×AGL(1,𝔽23)
unambiguous semidirect productD23⋊(C11×D21)
unambiguous semidirect product(C3×AGL(1,𝔽23))⋊D7
unambiguous semidirect product(D21×D23)⋊C11
unambiguous semidirect product(C7×AGL(1,𝔽23))⋊D3

Splittings

Fitting, socle, derived, HallC3×C7×C23 ⋊ C22×C11
HallC3×C7×C23⋊C11 ⋊ C22
HallD21×D23 ⋊ C11
HallC7×C23⋊C11 ⋊ C2×D3
HallC3×C23⋊C11 ⋊ C2×D7
HallC23⋊C11 ⋊ C2×D21
HallC7×C23 ⋊ C2×D3×C11
HallC3×C23 ⋊ C2×C11×D7
SylowC23 ⋊ C2×C11×D21
HallC3×C7 ⋊ C2×AGL(1,𝔽23)
SylowC7 ⋊ D3×AGL(1,𝔽23)
SylowC3 ⋊ D7×AGL(1,𝔽23)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C23C22×C11
LCSG ▷ C3×C7×C23
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 483

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21252, 44);