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Dic84⋊C3 #11759108

order1008
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productDic84⋊C3

Splittings

HallC3×ΓL(1,𝔽8) ⋊ Q16
SylowC7 ⋊ C3×Dic12

Subgroups

subgroupG/H
centerC2C4⋊(C3⋊AGL(1,𝔽7))
commutator, cosocleC3×C4×C7C22×C3
FrattiniC4C2×C3⋊AGL(1,𝔽7)
FittingC3×C7×C8C2×C3
socleC2×C3×C7C3×D4
prime radicalC2×C3×ΓL(1,𝔽8)D4
hypercenterC8C3⋊AGL(1,𝔽7)
hypocenterC3×C7C3×Q16
LCSG ▷ C3×C4×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2 ◁ C4 ◁ C8

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 336

Polycyclic presentation:

2^2,3,2^2,3,7|a^2=e,b^2=de,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^6,g^c=g^2

Conjugacy classes & character table

69 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1008, 279);