Finite Group Databasebeta

← Prev (#44540688) Next (#44540690) →

C2×D15×C529 #44540689

order31740
automorphism?
homologyAbelianization (H1) = C22×C529 · Schur multiplier (H2) = C2

Aliases

direct productC2×D15×C529
unambiguous semidirect product(C2×C3)⋊(D5×C529)
unambiguous semidirect product(C2×C5)⋊(D3×C529)

Splittings

FittingC2×C3×C5×C529 ⋊ C2
derived, HallC3×C5 ⋊ C22×C529
HallC3×C5×C529 ⋊ C22
HallC5×C529 ⋊ C2×D3
HallC3×C529 ⋊ C2×D5
SylowC5 ⋊ C2×D3×C529
SylowC3 ⋊ C2×D5×C529

Subgroups

subgroupG/H
center, hypercenterC2×C529D15
commutator, hypocenterC3×C5C22×C529
FrattiniC23C2×C23×D15
FittingC2×C3×C5×C529C2
socleC2×C3×C5×C23C2×C23
prime radicalC2×C23×D15C23
cosocleC3×C5×C23C22×C23
LCSG ▷ C3×C5
UCSC1 ◁ C2×C529

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15870

Conjugacy classes & character table

9522 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31740, 27);