Finite Group Databasebeta

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C8×#6758 #14280379

order1920
isoclinismisoclinic class of #6758
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4

Aliases

direct productC8×#6758

Splittings

HallC3×C5 ⋊ C8×M16
SylowC5 ⋊ C8×#208
SylowC3 ⋊ C8×#700

Subgroups

subgroupG/H
centerC2×C8C2×ΓL(1,𝔽16)
commutatorC2×C3×C5C2×C4×C8
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C4×C5×C8C4
socleC22×C3×C5C2×C42
prime radicalC22×C3×D5C42
cosocleC3×C4×Dic5C23
hypercenterC4×C8ΓL(1,𝔽16)
hypocenterC3×C5C8×M16
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C8 ◁ C4×C8

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 6077);