Finite Group Databasebeta

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C2×#11752438 #14320291

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#11752438
unambiguous semidirect productD5⋊#5220

Splittings

FittingC22×C3×C5×D4 ⋊ C4
HallC3×C5 ⋊ C2×#386
SylowC5 ⋊ C2×#5220
SylowC3 ⋊ C2×#65779

Subgroups

subgroupG/H
centerC23C22×ΓL(1,𝔽16)
commutatorC22×C3×C5C23×C4
FrattiniC22C23×ΓL(1,𝔽16)
FittingC22×C3×C5×D4C4
socleC23×C3×C5C22×C4
prime radicalC22×C3×D4×D5C2
cosocleC22×C3×D5C24
hypercenterC22×D4ΓL(1,𝔽16)
hypocenterC3×C5C2×#386
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

3152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45989);