Finite Group Databasebeta

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C3×C4×D5×C22⋊C4 #14319371

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC3×C4×D5×C22⋊C4

Splittings

FittingC3×C4×C5×C22⋊C4 ⋊ C2
HallC3×C5 ⋊ C2×C4×C22⋊C4
SylowC5 ⋊ C2×C3×C4×C22⋊C4

Subgroups

subgroupG/H
centerC22×C3×C4C22×D5
commutatorC2×C5C22×C3×C42
FrattiniC23C23×C3×D5
FittingC3×C4×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC24×C3×D5C22
cosocleC23×C5C24×C3
hypercenterC3×C4×C22⋊C4D5
hypocenterC5C2×C3×C4×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C22⋊C4

2720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45069);