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Q8×#6763 #14326124

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productQ8×#6763

Splittings

FittingC22×C3×C5×Q8 ⋊ C4
HallC3×C5 ⋊ Q8×C22⋊C4
SylowC5 ⋊ Q8×#217
SylowC3 ⋊ Q8×C22⋊AGL(1,𝔽5)

Subgroups

subgroupG/H
center, FrattiniC22C23×ΓL(1,𝔽16)
commutator, socleC22×C3×C5C23×C4
FittingC22×C3×C5×Q8C4
prime radicalC23×C3×D5C23
cosocleC22×C3×D5C24
hypercenterC22×Q8ΓL(1,𝔽16)
hypocenterC3×C5Q8×C22⋊C4
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×Q8

1640 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 51822);