Finite Group Databasebeta

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C2×C5×A4×C4⋊C4 #14511309

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC2×C5×A4×C4⋊C4
unambiguous semidirect product(C23×C4⋊C4)⋊(C3×C5)
unambiguous semidirect product(C23×C5×C4⋊C4)⋊C3

Splittings

Fitting, HallC23×C5×C4⋊C4 ⋊ C3
SylowC23×C4⋊C4 ⋊ C3×C5

Subgroups

subgroupG/H
centerC23×C5C22×A4
commutatorC23C22×C3×C4×C5
FrattiniC22C23×C5×A4
FittingC23×C5×C4⋊C4C3
socleC25×C5C22×C3
prime radicalC23×C5×A4C22
cosocleC24C23×C3×C5
hypercenterC2×C5×C4⋊C4A4
hypocenterC22C2×C3×C5×C4⋊C4
LCSG ▷ C23 ▷ C22
UCSC1 ◁ C23×C5 ◁ C2×C5×C4⋊C4

1136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

400 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237007);