Finite Group Databasebeta

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C3×C4⋊C4×C3⋊C8 #11784252

order1152
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×C4⋊C4×C3⋊C8

Splittings

SylowC32 ⋊ C8×C4⋊C4

Subgroups

subgroupG/H
centerC22×C3×C4C22×D3
commutatorC2×C3C2×C3×C4×C8
FrattiniC22×C4C22×C3×D3
FittingC32×C4×C4⋊C4C2
socle, prime radicalC23×C32C22×C4
cosocleC22×C3×C4C23×C3
hypercenterC3×C4×C4⋊C4D3
hypocenterC3C3×C8×C4⋊C4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C4⋊C4

689 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

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(1152, 18263);