Finite Group Databasebeta

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C25×C31×AGL(1,𝔽7) #45654402

order32550
automorphism?
homologyAbelianization (H1) = C2×C3×C25×C31 · Schur multiplier (H2) = C1

Aliases

direct productC25×C31×AGL(1,𝔽7)
unambiguous semidirect productD7⋊(C3×C25×C31)
unambiguous semidirect productΓL(1,𝔽8)⋊(C2×C25×C31)
unambiguous semidirect product(D7×C25)⋊(C3×C31)

Splittings

Fitting, HallC7×C25×C31 ⋊ C2×C3
derived, SylowC7 ⋊ C2×C3×C25×C31
HallΓL(1,𝔽8)×C25×C31 ⋊ C2
HallD7×C25×C31 ⋊ C3
HallΓL(1,𝔽8)×C31 ⋊ C2×C25
HallΓL(1,𝔽8)×C25 ⋊ C2×C31
HallD7×C31 ⋊ C3×C25
HallD7×C25 ⋊ C3×C31
HallC7×C31 ⋊ C2×C3×C25
HallC7×C25 ⋊ C2×C3×C31
HallΓL(1,𝔽8) ⋊ C2×C25×C31
HallD7 ⋊ C3×C25×C31

Subgroups

subgroupG/H
center, hypercenterC25×C31AGL(1,𝔽7)
commutator, hypocenterC7C2×C3×C25×C31
FrattiniC5C5×C31×AGL(1,𝔽7)
FittingC7×C25×C31C2×C3
socleC5×C7×C31C2×C3×C5
prime radicalC5×C31×AGL(1,𝔽7)C5
cosocleC5×C7C2×C3×C5×C31
LCSG ▷ C7
UCSC1 ◁ C25×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5425

Conjugacy classes & character table

5425 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32550, 38);