Finite Group Databasebeta

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C4×#91838 #14416651

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#91838

Splittings

FittingC3×C4×C5×#41 ⋊ C2
HallC3×C5 ⋊ C4×AGL(1,ℤ/8)
SylowC5 ⋊ C4×#949
SylowC3 ⋊ C4×#4095

Subgroups

subgroupG/H
centerC2×C4C2×#1220
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C4×C5×#41C2
socleC22×C3×C5C22×D4
prime radicalC2×#91838C2
cosocleC2×C3×C4×C5C24
hypercenterC4×#41D15
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

1096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 142349);