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D4×((C3⋊D3)⋊C3)⋊C4 #13151365

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

Aliases

direct productD4×((C3⋊D3)⋊C3)⋊C4

Splittings

SylowH(3,𝔽3) ⋊ C2×C4×D4

Subgroups

subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutatorC2×H(3,𝔽3)C23×C4
Frattini, socleC22×C3C22×D32
FittingC2×D4×H(3,𝔽3)C22
prime radicalC2×D4×(C3⋊D3)⋊C3C2
cosocleC22×H(3,𝔽3)C24
hypercenterC2×D4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)C2×C4×D4
LCSG ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C2×D4

1585 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 144

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 17428);