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C2×#11746763 #14294278

order1920
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#11746763

Splittings

FittingC22×C3×C5×C8 ⋊ C4
HallC3×C5 ⋊ C2×#336
SylowC5 ⋊ C2×#4550
SylowC3 ⋊ C2×(C2×AGL(1,𝔽5))⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×ΓL(1,𝔽16)
commutatorC2×C3×C5C2×C4×C8
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC22×C3×C5×C8C4
socleC23×C3×C5C42
prime radicalC23×C3×D5C2×C4
cosocleC2×C3×C4×D5C23
hypercenterC22×C8ΓL(1,𝔽16)
hypocenterC3×C5C2×#336
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C22×C8

1056 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

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, 19976);