Finite Group Databasebeta

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C2×ΓL(1,𝔽8)×Dic6 #11759476

order1008
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22

Aliases

direct productC2×ΓL(1,𝔽8)×Dic6
unambiguous semidirect product(C2×C3)⋊(Q8×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C7×Dic6)⋊C3

Splittings

HallC3×ΓL(1,𝔽8) ⋊ C2×Q8
SylowC7 ⋊ C2×C3×Dic6

Subgroups

subgroupG/H
centerC22C2×D3×ΓL(1,𝔽8)
commutator, cosocleC2×C3×C7C23×C3
FrattiniC2C22×D3×ΓL(1,𝔽8)
FittingC2×C3×C4×C7C2×C3
socleC22×C3×C7C22×C3
prime radicalC22×C3×ΓL(1,𝔽8)C22
hypercenterC2×C4D3×ΓL(1,𝔽8)
hypocenterC3×C7C2×C3×Q8
LCSG ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C22 ◁ C2×C4

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 336

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1008, 647);