Finite Group Databasebeta

← Prev (#37587793) Next (#37587795) →

C43⋊C3×D95 #37587794

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

Aliases

direct productC43⋊C3×D95
unambiguous semidirect productC5⋊(D19×C43⋊C3)

Splittings

Fitting, socle, derived, HallC5×C19×C43 ⋊ C2×C3
HallC5×C19×C43⋊C3 ⋊ C2
HallC43×D95 ⋊ C3
HallC19×C43⋊C3 ⋊ D5
HallC19×C43 ⋊ C3×D5
HallC5×C43⋊C3 ⋊ D19
HallC5×C43 ⋊ C3×D19
HallC5×C19 ⋊ C2×C43⋊C3
SylowC43 ⋊ C3×D95
SylowC19 ⋊ D5×C43⋊C3
SylowC5 ⋊ D19×C43⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C19×C43C2×C3
LCSG ▷ C5×C19×C43
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4085

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24510, 41);