Finite Group Databasebeta

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#104×Dic15 #14295579

order1920
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct product#104×Dic15

Splittings

HallC3×C5 ⋊ C4×#104
SylowC5 ⋊ Dic3×#104
SylowC3 ⋊ Dic5×#104

Subgroups

subgroupG/H
centerC2×C4D4×D15
commutatorC3×C4×C5C2×C42
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#104C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×C5×#41C22
cosocleC22×C3×C4×C5C23
hypercenterC2×#104D15
hypocenterC3×C5C4×#104
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21277);