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C2×Dic3×D5⋊C8 #14411188

order1920
isoclinismisoclinic class of D3×AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×Dic3×D5⋊C8

Splittings

derived, HallC3×C5 ⋊ C22×C4×C8
SylowC5 ⋊ C22×C8×Dic3
SylowC3 ⋊ C2×C4×D5⋊C8

Subgroups

subgroupG/H
center, hypercenterC22×C4D3×AGL(1,𝔽5)
commutator, hypocenterC3×C5C22×C4×C8
FrattiniC22C22×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC23×C3×C5C22×C4
prime radicalC23×C3×D5C2×C4
cosocleC2×C3×Dic5C24
LCSG ▷ C3×C5
UCSC1 ◁ C22×C4

1520 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, 136886);