Finite Group Databasebeta

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C2×Dic14⋊C9 #11758959

order1008
isoclinismisoclinic class of ΓL(1,𝔽8)⋊Q8
automorphism?
homologyAbelianization (H1) = C23×C9 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic14⋊C9
unambiguous semidirect product(C2×Dic14)⋊C9
unambiguous semidirect product(C2×C7⋊C9)⋊Q8

Splittings

HallC2×Dic14 ⋊ C9
HallC7⋊C9 ⋊ C2×Q8
SylowC7 ⋊ C2×Q8×C9

Subgroups

subgroupG/H
centerC22×C3C2×AGL(1,𝔽7)
commutatorC2×C7C23×C9
FrattiniC2×C3C22×AGL(1,𝔽7)
FittingC2×C3×C4×C7C2×C3
socle, prime radicalC22×C3×C7C22×C3
cosocleC2×C3×C7C23×C3
hypercenterC2×C3×C4AGL(1,𝔽7)
hypocenterC7C2×Q8×C9
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1008

Conjugacy classes & character table

114 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1008, 130);