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C5×C41×C3⋊AGL(1,𝔽7) #38788960

order25830
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C41 · Schur multiplier (H2) = C1

Aliases

direct productC5×C41×C3⋊AGL(1,𝔽7)
unambiguous semidirect productC3⋊(C5×C41×AGL(1,𝔽7))
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×D3×C41)
unambiguous semidirect productD21⋊(C3×C5×C41)
unambiguous semidirect product(C5×D21)⋊(C3×C41)
unambiguous semidirect product(C5×C41×D21)⋊C3

Splittings

Fitting, socleC3×C5×C7×C41 ⋊ C2×C3
derivedC3×C7 ⋊ C2×C3×C5×C41
HallC3×C5×ΓL(1,𝔽8)×C41 ⋊ C2
HallC3×ΓL(1,𝔽8)×C41 ⋊ C2×C5
HallC5×C7×C41 ⋊ C3×D3
HallC3×C5×ΓL(1,𝔽8) ⋊ C2×C41
HallC7×C41 ⋊ C3×C5×D3
HallC3×ΓL(1,𝔽8) ⋊ C2×C5×C41
HallC5×C7 ⋊ C3×D3×C41
SylowC7 ⋊ C3×C5×D3×C41

Subgroups

subgroupG/H
center, hypercenterC5×C41C3⋊AGL(1,𝔽7)
commutator, cosocle, hypocenterC3×C7C2×C3×C5×C41
FrattiniC1G
Fitting, socleC3×C5×C7×C41C2×C3
LCSG ▷ C3×C7
UCSC1 ◁ C5×C41

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4305

Conjugacy classes & character table

2460 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 64);