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C22×C3×#4004 #14412972

order1920
isoclinismisoclinic class of #700
automorphism?
homologyAbelianization (H1) = C23×C3×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×C3×#4004

Splittings

HallC3×C5 ⋊ C22×C4⋊C8
SylowC5 ⋊ C22×C3×C4⋊C8

Subgroups

subgroupG/H
centerC24×C3C2×AGL(1,𝔽5)
commutatorC2×C5C23×C3×C8
FrattiniC22C23×C3×AGL(1,𝔽5)
FittingC23×C3×C4×C5C4
socle, prime radicalC24×C3×C5C2×C4
cosocleC2×Dic5C24×C3
hypercenterC23×C3×C4AGL(1,𝔽5)
hypocenterC5C22×C3×C4⋊C8
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C23×C3×C4

1280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 138670);