Finite Group Databasebeta

← Prev (#37587776) Next (#37587778) →

C5×#19096726 #37587777

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

Aliases

direct productC5×#19096726

Splittings

Fitting, socle, HallC5×C19×C43 ⋊ C2×C3
derived, HallC19×C43 ⋊ C2×C3×C5
HallC5×#14578575 ⋊ C2
HallC5×C19×D43 ⋊ C3
Hall#14578575 ⋊ C2×C5
HallC19×D43 ⋊ C3×C5
HallC5×D43 ⋊ C19⋊C3
HallC5×C43 ⋊ C2×C19⋊C3
HallC5×C19 ⋊ D43⋊C3
HallD43 ⋊ C5×C19⋊C3
SylowC43 ⋊ C2×C5×C19⋊C3
SylowC19 ⋊ C5×D43⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#19096726
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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24510, 24);