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C5×ΓL(1,𝔽8)×C43⋊C7 #44539181

order31605
automorphism?
homologyAbelianization (H1) = C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)×C43⋊C7
unambiguous semidirect productC7⋊(C3×C5×C43⋊C7)
unambiguous semidirect product(C5×C7)⋊(C3×C43⋊C7)
unambiguous semidirect product(ΓL(1,𝔽8)×C43)⋊(C5×C7)
unambiguous semidirect product(C5×ΓL(1,𝔽8)×C43)⋊C7

Splittings

Fitting, socleC5×C7×C43 ⋊ C3×C7
derivedC7×C43 ⋊ C3×C5×C7
HallC5×C7×C43⋊C7 ⋊ C3
HallC7×C43⋊C7 ⋊ C3×C5
HallC5×C43 ⋊ C7×ΓL(1,𝔽8)
SylowC43 ⋊ C5×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)×C43⋊C7
commutator, cosocle, hypocenterC7×C43C3×C5×C7
FrattiniC1G
Fitting, socleC5×C7×C43C3×C7
LCSG ▷ C7×C43
UCSC1 ◁ C5

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1505

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31605, 12);