Finite Group Databasebeta

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C3×C4⋊C4×#168 #14296239

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×C4⋊C4×#168

Splittings

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

Subgroups

subgroupG/H
centerC22×C3×C4C22×D5
commutatorC2×C5C2×C3×C4×C8
FrattiniC22×C4C22×C3×D5
FittingC3×C4×C5×C4⋊C4C2
socle, prime radicalC23×C3×C5C22×C4
cosocleC22×C4×C5C23×C3
hypercenterC3×C4×C4⋊C4D5
hypocenterC5C3×C8×C4⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C4⋊C4

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21937);