Finite Group Databasebeta

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C4×#91833 #14322296

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

Aliases

direct productC4×#91833

Splittings

HallC3×C5 ⋊ C4×C4⋊Q8
SylowC5 ⋊ C4×#944
SylowC3 ⋊ C4×#4090

Subgroups

subgroupG/H
centerC22×C4C22×D15
commutatorC22×C3×C5C23×C4
FrattiniC23C23×D15
FittingC2×C3×C4×C5×Q8C2
socle, prime radical, cosocleC23×C3×C5C24
hypercenterC2×C4×Q8D15
hypocenterC3×C5C4×C4⋊Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C4×Q8

1176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 47994);