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C34×AGL(1,𝔽7) #72249107

order3402
automorphism?
homologyAbelianization (H1) = C2×C35 · Schur multiplier (H2) = C310

Aliases

direct productC34×AGL(1,𝔽7)

Splittings

Fitting, socleC34×C7 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C35
HallC34×ΓL(1,𝔽8) ⋊ C2
HallD7 ⋊ C35

Subgroups

subgroupG/H
center, hypercenterC34AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C2×C35
FrattiniC1G
Fitting, socleC34×C7C2×C3
LCSG ▷ C7
UCSC1 ◁ C34

10656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 567

Conjugacy classes & character table

567 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×AGL(1,𝔽7)×AΣL(1,𝔽27), AGL(1,𝔽7)×C32⋊H(3,𝔽3), AGL(1,𝔽7)×#6891, …
maximal normal subgroup ofC3×AGL(1,𝔽7)×AΣL(1,𝔽27), AGL(1,𝔽7)×C32⋊H(3,𝔽3), AGL(1,𝔽7)×#6891, …
maximal quotient ofAGL(1,𝔽7)×3−1+4

GAP

Past the SmallGroups library coverage — no SmallGroups id.