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AGL(1,𝔽7)×3−1+4 #72249128

order10206
automorphism?
homologyAbelianization (H1) = C2×C35 · Schur multiplier (H2) = C39

Aliases

direct productAGL(1,𝔽7)×3−1+4

Splittings

FittingC7×3−1+4 ⋊ C2×C3
HallΓL(1,𝔽8)×3−1+4 ⋊ C2
HallD7 ⋊ C3×3−1+4
SylowC7 ⋊ C2×C3×3−1+4

Subgroups

subgroupG/H
center, FrattiniC3C34×AGL(1,𝔽7)
commutator, socle, cosocleC3×C7C2×C35
FittingC7×3−1+4C2×C3
prime radicalC3×H(3,𝔽3)×AGL(1,𝔽7)C3
hypercenter3−1+4AGL(1,𝔽7)
hypocenterC7C2×C3×3−1+4
LCSG ▷ C3×C7 ▷ C7
UCSC1 ◁ C3 ◁ 3−1+4

11176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 189

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,𝔽7)×#10624749, AGL(1,𝔽7)×#4207⋊C3
maximal normal subgroup ofAGL(1,𝔽7)×#10624749, AGL(1,𝔽7)×#4207⋊C3

GAP

Past the SmallGroups library coverage — no SmallGroups id.