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C22⋊ΓL(1,𝔽8)×C71⋊C5 #44447192

order29820
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC22⋊ΓL(1,𝔽8)×C71⋊C5
unambiguous semidirect productC22⋊(ΓL(1,𝔽8)×C71⋊C5)
unambiguous semidirect productC7⋊(A4×C71⋊C5)
unambiguous semidirect productC71⋊(C5×C22⋊ΓL(1,𝔽8))
unambiguous semidirect product(C22×C71⋊C5)⋊ΓL(1,𝔽8)
unambiguous semidirect product(C7×C71⋊C5)⋊A4
unambiguous semidirect product(C71×C22⋊ΓL(1,𝔽8))⋊C5

Splittings

Fitting, socle, derived, HallC22×C7×C71 ⋊ C3×C5
HallC22×C7×C71⋊C5 ⋊ C3
HallC71×C22⋊ΓL(1,𝔽8) ⋊ C5
HallC7×C71⋊C5 ⋊ A4
HallC22×C71⋊C5 ⋊ ΓL(1,𝔽8)
HallC7×C71 ⋊ C5×A4
HallC22×C71 ⋊ C5×ΓL(1,𝔽8)
SylowC71 ⋊ C5×C22⋊ΓL(1,𝔽8)
HallC22×C7 ⋊ C3×C71⋊C5
SylowC7 ⋊ A4×C71⋊C5
SylowC22 ⋊ ΓL(1,𝔽8)×C71⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC22×C7×C71C3×C5
LCSG ▷ C22×C7×C71
UCSC1

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1988

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 80);