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#101×AGL(1,𝔽7) #13051650

order1344
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct product#101×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×#101)
unambiguous semidirect product(D7×#101)⋊C3

Splittings

FittingC7×#101 ⋊ C2×C3
HallD7×#101 ⋊ C3
HallΓL(1,𝔽8) ⋊ C2×#101
SylowC7 ⋊ C2×C3×#101

Subgroups

subgroupG/H
centerC2C22⋊C4×AGL(1,𝔽7)
commutatorC22×C7C22×C3×C4
FrattiniC2×C4C22×AGL(1,𝔽7)
FittingC7×#101C2×C3
socleC2×C7C2×C3×C22⋊C4
prime radicalC22×AGL(1,𝔽7)C2×C4
cosocleC2×C4×C7C23×C3
hypercenter#101AGL(1,𝔽7)
hypocenterC7C2×C3×#101
LCSG ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

292 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 112

Conjugacy classes & character table

77 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×#413, AGL(1,𝔽7)×#454
maximal normal subgroup ofAGL(1,𝔽7)×#413, AGL(1,𝔽7)×#454

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 939);