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C4⋊C4×#1084 #13144347

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

Aliases

direct productC4⋊C4×#1084

Splittings

SylowH(3,𝔽3) ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
center, Frattini, socleC23×C3C22×C3⋊D3
commutatorC2×H(3,𝔽3)C2×C42
FittingC2×C4⋊C4×H(3,𝔽3)C2
prime radical, cosocleC23×H(3,𝔽3)C23
hypercenterC2×C3×C4⋊C4C3⋊D3
hypocenterH(3,𝔽3)C4×C4⋊C4
LCSG ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C23×C3 ◁ C2×C3×C4⋊C4

1067 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 10410);