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C4×D7⋊C27 #13094111

order1512
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C2×C4×C27 · Schur multiplier (H2) = C2

Aliases

direct productC4×D7⋊C27
unambiguous semidirect productD7⋊(C4×C27)
unambiguous semidirect product(C4×D7)⋊C27

Splittings

derived, SylowC7 ⋊ C2×C4×C27
HallC7⋊C27 ⋊ C2×C4
HallC4×D7 ⋊ C27

Subgroups

subgroupG/H
center, hypercenterC4×C9AGL(1,𝔽7)
commutator, hypocenterC7C2×C4×C27
FrattiniC2×C9C2×AGL(1,𝔽7)
FittingC4×C7×C9C2×C3
socleC2×C3×C7C22×C9
prime radicalC2×C3×D7C2×C9
cosocleC2×C7×C9C22×C3
LCSG ▷ C7
UCSC1 ◁ C4×C9

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 756

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1512, 8);