Finite Group Databasebeta

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C22×#91236 #14412254

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×#91236
unambiguous semidirect productD5⋊(C2×#832)

Splittings

FittingC22×C3×C5×D4 ⋊ C4
HallC3×C5 ⋊ C22×#102
SylowC5 ⋊ C22×#832
SylowC3 ⋊ C22×#4007

Subgroups

subgroupG/H
centerC23#6763
commutatorC3×C4×C5C23×C4
FrattiniC4C23×ΓL(1,𝔽16)
FittingC22×C3×C5×D4C4
socleC23×C3×C5C22⋊C4
prime radicalC22×C3×D4×D5C2
cosocleC3×C4×D5C24
hypercenterC22×D4ΓL(1,𝔽16)
hypocenterC3×C5C22×#102
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

2144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

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, 137952);