Finite Group Databasebeta

← Prev (#46852864) Next (#46852866) →

C3×D5×D581 #46852865

order34860
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×D581
unambiguous semidirect product(D5×C83)⋊(C3×D7)

Splittings

Fitting, socle, HallC3×C5×C7×C83 ⋊ C22
derived, HallC5×C7×C83 ⋊ C22×C3
HallC3×C7×C83 ⋊ C2×D5
HallC3×C5×C83 ⋊ C2×D7
HallC7×C83 ⋊ C2×C3×D5
HallC5×C83 ⋊ C2×C3×D7
HallC3×C83 ⋊ D5×D7
HallC3×C5×C7 ⋊ C2×D83
SylowC83 ⋊ C3×D5×D7
HallC5×C7 ⋊ C2×C3×D83
HallC3×C7 ⋊ D5×D83
HallC3×C5 ⋊ C2×D581
SylowC7 ⋊ C3×D5×D83
SylowC5 ⋊ C2×C3×D581

Subgroups

subgroupG/H
center, hypercenterC3D5×D581
commutator, cosocle, hypocenterC5×C7×C83C22×C3
FrattiniC1G
Fitting, socleC3×C5×C7×C83C22
LCSG ▷ C5×C7×C83
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8715

Conjugacy classes & character table

3504 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34860, 53);