Finite Group Databasebeta

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C5×C43×D19⋊C3 #37587779

order24510
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C43 · Schur multiplier (H2) = C1

Aliases

direct productC5×C43×D19⋊C3
unambiguous semidirect productD19⋊(C3×C5×C43)
unambiguous semidirect product(C19⋊C3)⋊(C2×C5×C43)
unambiguous semidirect product(C5×D19)⋊(C3×C43)

Splittings

Fitting, socle, HallC5×C19×C43 ⋊ C2×C3
derived, SylowC19 ⋊ C2×C3×C5×C43
HallC5×C43×C19⋊C3 ⋊ C2
HallC5×D19×C43 ⋊ C3
HallC43×C19⋊C3 ⋊ C2×C5
HallD19×C43 ⋊ C3×C5
HallC19×C43 ⋊ C2×C3×C5
HallC5×C19⋊C3 ⋊ C2×C43
HallC5×D19 ⋊ C3×C43
HallC5×C19 ⋊ C2×C3×C43
HallC19⋊C3 ⋊ C2×C5×C43
HallD19 ⋊ C3×C5×C43

Subgroups

subgroupG/H
center, hypercenterC5×C43D19⋊C3
commutator, cosocle, hypocenterC19C2×C3×C5×C43
FrattiniC1G
Fitting, socleC5×C19×C43C2×C3
LCSG ▷ C19
UCSC1 ◁ C5×C43

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4085

Conjugacy classes & character table

1935 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24510, 26);