Finite Group Databasebeta

← Prev (#44445808) Next (#44445810) →

C5×C23⋊(D43⋊C3) #44445809

order29670
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C23⋊(D43⋊C3)
unambiguous semidirect productC23⋊(C5×D43⋊C3)
unambiguous semidirect product(C43⋊C3)⋊(C5×D23)
unambiguous semidirect productD989⋊(C3×C5)
unambiguous semidirect product(C5×D989)⋊C3

Splittings

Fitting, socle, HallC5×C23×C43 ⋊ C2×C3
derived, HallC23×C43 ⋊ C2×C3×C5
HallC5×C23×C43⋊C3 ⋊ C2
HallC5×D989 ⋊ C3
HallC23×C43⋊C3 ⋊ C2×C5
HallD989 ⋊ C3×C5
HallC5×C43⋊C3 ⋊ D23
HallC5×C43 ⋊ C3×D23
HallC43⋊C3 ⋊ C5×D23
HallC5×C23 ⋊ D43⋊C3
SylowC43 ⋊ C3×C5×D23
SylowC23 ⋊ C5×D43⋊C3

Subgroups

subgroupG/H
center, hypercenterC5C23⋊(D43⋊C3)
commutator, cosocle, hypocenterC23×C43C2×C3×C5
FrattiniC1G
Fitting, socleC5×C23×C43C2×C3
LCSG ▷ C23×C43
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4945

Conjugacy classes & character table

1000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29670, 20);