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D5×AGL(1,𝔽7)×C79 #45684443

order33180
automorphism?
homologyAbelianization (H1) = C22×C3×C79 · Schur multiplier (H2) = C2

Aliases

direct productD5×AGL(1,𝔽7)×C79
unambiguous semidirect productD7⋊(C3×D5×C79)
unambiguous semidirect product(D5×D7)⋊(C3×C79)
unambiguous semidirect product(C5×AGL(1,𝔽7))⋊(C2×C79)
unambiguous semidirect product(D5×ΓL(1,𝔽8))⋊(C2×C79)
unambiguous semidirect product(C5⋊AGL(1,𝔽7))⋊(C2×C79)

Splittings

Fitting, socle, HallC5×C7×C79 ⋊ C22×C3
derived, HallC5×C7 ⋊ C22×C3×C79
HallD5×D7×C79 ⋊ C3
HallC5×ΓL(1,𝔽8)×C79 ⋊ C22
HallΓL(1,𝔽8)×C79 ⋊ C2×D5
HallC7×C79 ⋊ C2×C3×D5
HallC5×C79 ⋊ C2×AGL(1,𝔽7)
HallD5×D7 ⋊ C3×C79
HallC5×ΓL(1,𝔽8) ⋊ C22×C79
HallΓL(1,𝔽8) ⋊ C2×D5×C79
SylowC7 ⋊ C2×C3×D5×C79
SylowC5 ⋊ C2×AGL(1,𝔽7)×C79

Subgroups

subgroupG/H
center, hypercenterC79D5×AGL(1,𝔽7)
commutator, cosocle, hypocenterC5×C7C22×C3×C79
FrattiniC1G
Fitting, socleC5×C7×C79C22×C3
LCSG ▷ C5×C7
UCSC1 ◁ C79

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2765

Conjugacy classes & character table

2212 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33180, 74);