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#41×(C3⋊Dic3)⋊C3 #13153716

order1728
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25×C3

Aliases

direct product#41×(C3⋊Dic3)⋊C3

Splittings

SylowH(3,𝔽3) ⋊ C4×#41

Subgroups

subgroupG/H
centerC2×C4C22×(C3⋊D3)⋊C3
commutatorC2×C32C23×C3×C4
Frattini, socleC22×C3C23×C3×D3
Fitting, prime radicalC2×#41×H(3,𝔽3)C2
cosocleC22×C32C24×C3
hypercenterC2×#41(C3⋊D3)⋊C3
hypocenterC32C3×C4×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×#41

1249 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

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, 19779);