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C4⋊C4×C3⋊(C3⋊Dic3) #13163608

order1728
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C33×C4

Aliases

direct productC4⋊C4×C3⋊(C3⋊Dic3)

Splittings

SylowC33 ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C22×C3⋊(C3⋊D3)
commutatorC2×C33C2×C42
FittingC2×C33×C4⋊C4C2
socle, prime radical, cosocleC23×C33C23
hypercenterC2×C4⋊C4C3⋊(C3⋊D3)
hypocenterC33C4×C4⋊C4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C23 ◁ C2×C4⋊C4

2716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1728

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 29671);