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D3×D7×C22⋊C4 #13058468

order1344
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD3×D7×C22⋊C4

Splittings

FittingC3×C7×C22⋊C4 ⋊ C22
HallC3×C7 ⋊ C22×C22⋊C4
SylowC7 ⋊ C2×D3×C22⋊C4
SylowC3 ⋊ C2×D7×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D3×D7
commutatorC2×C3×C7C23×C4
FittingC3×C7×C22⋊C4C22
socle, cosocleC22×C3×C7C24
prime radicalC23×D3×D7C2
hypercenterC22⋊C4D3×D7
hypocenterC3×C7C22×C22⋊C4
LCSG ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C22⋊C4

1348 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×D7×#120, D3×C22⋊C4×AGL(1,𝔽7), D3×D7×#99, …
maximal normal subgroup ofD3×D7×#120, D3×C22⋊C4×AGL(1,𝔽7), D3×D7×#99
maximal quotient ofD3×D7×#99, D3×D7×#100, D3×D7×#104, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 7757);