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C4⋊(C3⋊(C7⋊C16)) #13051364

order1344
automorphism?
homologyAbelianization (H1) = C2×C16 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productC4⋊(C3⋊(C7⋊C16))

Splittings

HallC3×C7 ⋊ C4⋊C16
SylowC7 ⋊ C4⋊(C3⋊C16)
SylowC3 ⋊ C4⋊(C7⋊C16)

Subgroups

subgroupG/H
center, FrattiniC2×C8C2×D21
commutatorC2×C3×C7C2×C16
FittingC3×C4×C7×C8C2
socle, prime radicalC22×C3×C7C2×C8
cosocleC2×C3×C7×C8C22
hypercenterC4×C8D21
hypocenterC3×C7C4⋊C16
LCSG ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2×C8 ◁ C4×C8

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1344

Polycyclic presentation:

2^6,3,7|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^a=g^2,h^a=h^6

Conjugacy classes & character table

360 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 653);