Finite Group Databasebeta

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D21×C23⋊C11 #24922317

order10626
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productD21×C23⋊C11
unambiguous semidirect productC3⋊(D7×C23⋊C11)
unambiguous semidirect productC7⋊(D3×C23⋊C11)
unambiguous semidirect product(C23×D21)⋊C11

Splittings

Fitting, socle, derived, HallC3×C7×C23 ⋊ C2×C11
HallC3×C7×C23⋊C11 ⋊ C2
HallC7×C23⋊C11 ⋊ D3
HallC23×D21 ⋊ C11
HallC3×C23⋊C11 ⋊ D7
HallC7×C23 ⋊ D3×C11
HallC3×C23 ⋊ C11×D7
SylowC23 ⋊ C11×D21
HallC3×C7 ⋊ C2×C23⋊C11
SylowC7 ⋊ D3×C23⋊C11
SylowC3 ⋊ D7×C23⋊C11

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C23C2×C11
LCSG ▷ C3×C7×C23
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD21×AGL(1,𝔽23), D21⋊AGL(1,𝔽23), D3×D7×C23⋊C11, …
maximal normal subgroup ofD21×AGL(1,𝔽23), D21⋊AGL(1,𝔽23), D3×D7×C23⋊C11, …
maximal quotient ofDic21×C23⋊C11, C2×D21×C23⋊C11, D63×C23⋊C11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10626, 25);