Finite Group Databasebeta

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C23×(C43⋊C3)⋊C7 #35209343

order20769
automorphism?
homologyAbelianization (H1) = C3×C7×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×(C43⋊C3)⋊C7
unambiguous semidirect product(C43⋊C3)⋊(C7×C23)
unambiguous semidirect product(C43⋊C7)⋊(C3×C23)
unambiguous semidirect product(C23×C43⋊C3)⋊C7
unambiguous semidirect product(C23×C43⋊C7)⋊C3

Splittings

Fitting, socle, HallC23×C43 ⋊ C3×C7
derived, SylowC43 ⋊ C3×C7×C23
HallC23×C43⋊C7 ⋊ C3
HallC23×C43⋊C3 ⋊ C7
HallC43⋊C7 ⋊ C3×C23
HallC43⋊C3 ⋊ C7×C23

Subgroups

subgroupG/H
center, hypercenterC23(C43⋊C3)⋊C7
commutator, cosocle, hypocenterC43C3×C7×C23
FrattiniC1G
Fitting, socleC23×C43C3×C7
LCSG ▷ C43
UCSC1 ◁ C23

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 989

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20769, 7);