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C5×C71×C22⋊ΓL(1,𝔽8) #44447272

order29820
automorphism?
homologyAbelianization (H1) = C3×C5×C71 · Schur multiplier (H2) = C2

Aliases

direct productC5×C71×C22⋊ΓL(1,𝔽8)
unambiguous semidirect productC22⋊(C5×ΓL(1,𝔽8)×C71)
unambiguous semidirect productC7⋊(C5×A4×C71)
unambiguous semidirect product(C22×C5)⋊(ΓL(1,𝔽8)×C71)
unambiguous semidirect product(C5×C7)⋊(A4×C71)
unambiguous semidirect product(C22×C5×C71)⋊ΓL(1,𝔽8)
unambiguous semidirect product(C5×C7×C71)⋊A4

Splittings

Fitting, socle, HallC22×C5×C7×C71 ⋊ C3
derived, HallC22×C7 ⋊ C3×C5×C71
HallC5×C7×C71 ⋊ A4
HallC22×C7×C71 ⋊ C3×C5
HallC22×C5×C71 ⋊ ΓL(1,𝔽8)
HallC7×C71 ⋊ C5×A4
HallC22×C71 ⋊ C5×ΓL(1,𝔽8)
HallC22×C5×C7 ⋊ C3×C71
HallC5×C7 ⋊ A4×C71
HallC22×C5 ⋊ ΓL(1,𝔽8)×C71
SylowC7 ⋊ C5×A4×C71
SylowC22 ⋊ C5×ΓL(1,𝔽8)×C71

Subgroups

subgroupG/H
center, hypercenterC5×C71C22⋊ΓL(1,𝔽8)
commutator, cosocle, hypocenterC22×C7C3×C5×C71
FrattiniC1G
Fitting, socleC22×C5×C7×C71C3
LCSG ▷ C22×C7
UCSC1 ◁ C5×C71

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9940

Conjugacy classes & character table

4260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 160);