Finite Group Databasebeta

← Prev (#14415688) Next (#14415690) →

M16×D60 #14415689

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productM16×D60

Splittings

FittingC3×C4×C5×M16 ⋊ C2
HallC3×C5 ⋊ D4×M16
SylowC5 ⋊ M16×D12
SylowC3 ⋊ M16×D20

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D15
commutator, socleC22×C3×C5C23×C4
FittingC3×C4×C5×M16C2
prime radicalC22×D60C4
cosocleC2×C3×C4×C5C24
hypercenterC4×M16D15
hypocenterC3×C5D4×M16
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C4×M16

1088 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 141387);