Finite Group Databasebeta

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C4⋊C4×C3⋊#168 #14296240

order1920
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4⋊C4×C3⋊#168

Splittings

HallC3×C5 ⋊ C8×C4⋊C4
SylowC5 ⋊ C4⋊C4×C3⋊C8
SylowC3 ⋊ C4⋊C4×#168

Subgroups

subgroupG/H
center, FrattiniC22×C4C22×D15
commutatorC2×C3×C5C2×C4×C8
FittingC3×C4×C5×C4⋊C4C2
socle, prime radicalC23×C3×C5C22×C4
cosocleC22×C3×C4×C5C23
hypercenterC4×C4⋊C4D15
hypocenterC3×C5C8×C4⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21938);