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C2×AGL(1,𝔽7)×C373 #44531278

order31332
automorphism?
homologyAbelianization (H1) = C22×C3×C373 · Schur multiplier (H2) = C2

Aliases

direct productC2×AGL(1,𝔽7)×C373
unambiguous semidirect productD7⋊(C2×C3×C373)
unambiguous semidirect productΓL(1,𝔽8)⋊(C22×C373)
unambiguous semidirect product(C2×D7)⋊(C3×C373)
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C2×C373)

Splittings

Fitting, socleC2×C7×C373 ⋊ C2×C3
derived, SylowC7 ⋊ C22×C3×C373
HallC2×D7×C373 ⋊ C3
HallΓL(1,𝔽8)×C373 ⋊ C22
HallC7×C373 ⋊ C22×C3
HallC2×D7 ⋊ C3×C373
HallΓL(1,𝔽8) ⋊ C22×C373

Subgroups

subgroupG/H
center, hypercenterC2×C373AGL(1,𝔽7)
commutator, cosocle, hypocenterC7C22×C3×C373
FrattiniC1G
Fitting, socleC2×C7×C373C2×C3
LCSG ▷ C7
UCSC1 ◁ C2×C373

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5222

Conjugacy classes & character table

5222 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31332, 39);