Finite Group Databasebeta

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C22×C3×#3993 #14413249

order1920
isoclinismisoclinic class of #3993
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×C3×#3993
unambiguous semidirect productD5⋊(C2×C3×#106)

Splittings

FittingC22×C3×C5×C8 ⋊ C4
HallC3×C5 ⋊ C22×#106
SylowC5 ⋊ C22×C3×#106

Subgroups

subgroupG/H
centerC23×C3C4⋊AGL(1,𝔽5)
commutatorC4×C5C23×C3×C4
FrattiniC4C23×C3×AGL(1,𝔽5)
FittingC22×C3×C5×C8C4
socleC23×C3×C5C4⋊C4
prime radicalC23×C3×D5D4
cosocleC4×D5C24×C3
hypercenterC22×C3×C8AGL(1,𝔽5)
hypocenterC5C22×C3×#106
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4 ◁ C22×C3×C8

1200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 138947);