Finite Group Databasebeta

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Q8×#6669 #14327248

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

Aliases

direct productQ8×#6669

Splittings

HallC3×C5 ⋊ Q8×C4⋊C4
SylowC5 ⋊ Q8×Dic3⋊C4
SylowC3 ⋊ Q8×#683

Subgroups

subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×Q8C22
socle, prime radical, cosocleC23×C3×C5C24
hypercenterC22×Q8D3×D5
hypocenterC3×C5Q8×C4⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

1136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 52946);