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C2×C7⋊(Q8⋊C9) #11759010

order1008
isoclinismisoclinic class of C7⋊SL(2,𝔽3)
automorphism?
homologyAbelianization (H1) = C2×C9 · Schur multiplier (H2) = C1

Aliases

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

Splittings

derivedC7×Q8 ⋊ C2×C9
HallC2×C7×Q8 ⋊ C9
SylowC2×Q8 ⋊ C7⋊C9
SylowC7 ⋊ C2×Q8⋊C9

Subgroups

subgroupG/H
center, hypercenterC22×C3C22⋊ΓL(1,𝔽8)
commutator, hypocenterC7×Q8C2×C9
FrattiniC2×C3C2×C22⋊ΓL(1,𝔽8)
FittingC2×C3×C7×Q8C3
socle, prime radicalC22×C3×C7A4
cosocleC3×C7×Q8C2×C3
LCSG ▷ C7×Q8
UCSC1 ◁ C22×C3

58 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1008

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1008, 181);