Finite Group Databasebeta

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C5×(C19⋊C3)⋊D43 #37587783

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

Aliases

direct productC5×(C19⋊C3)⋊D43
unambiguous semidirect product(C19⋊C3)⋊(C5×D43)

Splittings

Fitting, socle, HallC5×C19×C43 ⋊ C2×C3
derived, HallC19×C43 ⋊ C2×C3×C5
HallC5×C43×C19⋊C3 ⋊ C2
HallC5×D817 ⋊ C3
HallC43×C19⋊C3 ⋊ C2×C5
HallD817 ⋊ C3×C5
HallC5×C19⋊C3 ⋊ D43
HallC5×C43 ⋊ D19⋊C3
HallC5×C19 ⋊ C3×D43
HallC19⋊C3 ⋊ C5×D43
SylowC43 ⋊ C5×D19⋊C3
SylowC19 ⋊ C3×C5×D43

Subgroups

subgroupG/H
center, hypercenterC5(C19⋊C3)⋊D43
commutator, cosocle, hypocenterC19×C43C2×C3×C5
FrattiniC1G
Fitting, socleC5×C19×C43C2×C3
LCSG ▷ C19×C43
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4085

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24510, 30);