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C4×D4×C3⋊(C3⋊D3) #13179671

order1728
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C33

Aliases

direct productC4×D4×C3⋊(C3⋊D3)

Splittings

FittingC33×C4×D4 ⋊ C2
SylowC33 ⋊ C2×C4×D4

Subgroups

subgroupG/H
centerC2×C4C22×C3⋊(C3⋊D3)
commutatorC2×C33C23×C4
FrattiniC22C23×C3⋊(C3⋊D3)
FittingC33×C4×D4C2
socle, cosocleC22×C33C24
prime radicalC2×D4×C3⋊(C3⋊D3)C2
hypercenterC4×D4C3⋊(C3⋊D3)
hypocenterC33C2×C4×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C4 ◁ C4×D4

5964 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 432

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3⋊(C3⋊D3)×#442, C4×D3×D4×C3⋊D3, #72268946
maximal normal subgroup ofC3⋊(C3⋊D3)×#442, C4×D3×D4×C3⋊D3, #72268946
maximal quotient ofC3⋊(C3⋊D3)×#442

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 45734);