Finite Group Databasebeta

← Prev (#37587771) Next (#37587773) →

C43×D285 #37587772

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

Aliases

direct productC43×D285
unambiguous semidirect productC3⋊(C43×D95)
unambiguous semidirect productC5⋊(C43×D57)
unambiguous semidirect productC19⋊(D15×C43)

Splittings

Fitting, socle, HallC3×C5×C19×C43 ⋊ C2
derived, HallC3×C5×C19 ⋊ C2×C43
HallC5×C19×C43 ⋊ D3
HallC3×C19×C43 ⋊ D5
HallC19×C43 ⋊ D15
HallC3×C5×C43 ⋊ D19
HallC5×C43 ⋊ D57
HallC3×C43 ⋊ D95
HallC5×C19 ⋊ D3×C43
HallC3×C19 ⋊ D5×C43
SylowC19 ⋊ D15×C43
HallC3×C5 ⋊ D19×C43
SylowC5 ⋊ C43×D57
SylowC3 ⋊ C43×D95

Subgroups

subgroupG/H
center, hypercenterC43D285
commutator, cosocle, hypocenterC3×C5×C19C2×C43
FrattiniC1G
Fitting, socleC3×C5×C19×C43C2
LCSG ▷ C3×C5×C19
UCSC1 ◁ C43

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12255

Conjugacy classes & character table

6192 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24510, 19);