Finite Group Databasebeta

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C23×C3⋊(D31⋊C5) #36339028

order21390
automorphism?
homologyAbelianization (H1) = C2×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×C3⋊(D31⋊C5)
unambiguous semidirect productC3⋊(C23×D31⋊C5)
unambiguous semidirect productΓL(1,𝔽32)⋊(D3×C23)
unambiguous semidirect productD93⋊(C5×C23)
unambiguous semidirect product(C23×D93)⋊C5

Splittings

Fitting, socle, HallC3×C23×C31 ⋊ C2×C5
derived, HallC3×C31 ⋊ C2×C5×C23
HallC3×C23×ΓL(1,𝔽32) ⋊ C2
HallC23×D93 ⋊ C5
HallC23×ΓL(1,𝔽32) ⋊ D3
HallC23×C31 ⋊ C5×D3
HallC3×ΓL(1,𝔽32) ⋊ C2×C23
HallD93 ⋊ C5×C23
HallΓL(1,𝔽32) ⋊ D3×C23
HallC3×C23 ⋊ D31⋊C5
SylowC31 ⋊ C5×D3×C23
SylowC3 ⋊ C23×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC23C3⋊(D31⋊C5)
commutator, cosocle, hypocenterC3×C31C2×C5×C23
FrattiniC1G
Fitting, socleC3×C23×C31C2×C5
LCSG ▷ C3×C31
UCSC1 ◁ C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2139

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21390, 24);