Finite Group Databasebeta

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C4⋊C4×C3⋊Dic9 #13144319

order1728
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C3×C4

Aliases

direct productC4⋊C4×C3⋊Dic9

Splittings

SylowC3×C9 ⋊ C4×C4⋊C4

Subgroups

subgroupG/H
centerC23C22×C3⋊D9
commutatorC2×C3×C9C2×C42
FrattiniC23×C3C22×C3⋊D3
FittingC2×C3×C9×C4⋊C4C2
socle, prime radicalC23×C32C22×D3
cosocleC23×C3×C9C23
hypercenterC2×C4⋊C4C3⋊D9
hypocenterC3×C9C4×C4⋊C4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C23 ◁ C2×C4⋊C4

970 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, 10382);