Finite Group Databasebeta

← Prev (#44445800) Next (#44445802) →

C5×C43×D69 #44445801

order29670
automorphism?
homologyAbelianization (H1) = C2×C5×C43 · Schur multiplier (H2) = C1

Aliases

direct productC5×C43×D69
unambiguous semidirect productC3⋊(C5×C43×D23)
unambiguous semidirect productC23⋊(C5×D3×C43)

Splittings

Fitting, socle, HallC3×C5×C23×C43 ⋊ C2
derived, HallC3×C23 ⋊ C2×C5×C43
HallC5×C23×C43 ⋊ D3
HallC3×C23×C43 ⋊ C2×C5
HallC23×C43 ⋊ C5×D3
HallC3×C5×C43 ⋊ D23
HallC3×C5×C23 ⋊ C2×C43
HallC3×C43 ⋊ C5×D23
HallC5×C23 ⋊ D3×C43
SylowC23 ⋊ C5×D3×C43
HallC3×C5 ⋊ C43×D23
SylowC3 ⋊ C5×C43×D23

Subgroups

subgroupG/H
center, hypercenterC5×C43D69
commutator, cosocle, hypocenterC3×C23C2×C5×C43
FrattiniC1G
Fitting, socleC3×C5×C23×C43C2
LCSG ▷ C3×C23
UCSC1 ◁ C5×C43

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14835

Conjugacy classes & character table

7740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29670, 12);