Finite Group Databasebeta

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C3×D5×#421 #14412834

order1920
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC3×D5×#421

Splittings

FittingC3×C5×#421 ⋊ C2
HallC3×C5 ⋊ C2×#421
SylowC5 ⋊ C2×C3×#421

Subgroups

subgroupG/H
centerC3×C4C2×D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#421C2
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×C3×D5×#41C2
cosocleC2×C4×C5C24×C3
hypercenterC3×#421D5
hypocenterC5C2×C3×#421
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C22×C3×C4 ◁ C3×#421

1544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 138532);