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C4×ΓL(1,𝔽8)⋊D9 #13094302

order1512
isoclinismisoclinic class of ΓL(1,𝔽8)⋊D9
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC4×ΓL(1,𝔽8)⋊D9

Splittings

FittingC4×C7×C9 ⋊ C2×C3
derivedC7×C9 ⋊ C2×C3×C4
HallC9×ΓL(1,𝔽8) ⋊ C2×C4
SylowC7 ⋊ C3×C4×D9

Subgroups

subgroupG/H
center, hypercenterC4ΓL(1,𝔽8)⋊D9
commutator, hypocenterC7×C9C2×C3×C4
FrattiniC2×C3C2×C3⋊AGL(1,𝔽7)
FittingC4×C7×C9C2×C3
socleC2×C3×C7C2×C3×D3
prime radicalC2×ΓL(1,𝔽8)⋊D9C2
cosocleC2×C7×C9C22×C3
LCSG ▷ C7×C9
UCSC1 ◁ C4

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 252

Conjugacy classes & character table

108 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×D9×AGL(1,𝔽7), D4×ΓL(1,𝔽8)⋊D9, #72278028
maximal normal subgroup ofC4×D9×AGL(1,𝔽7), D4×ΓL(1,𝔽8)⋊D9, #72278028

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1512, 199);