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C4×ΓL(1,𝔽8)×C71⋊C5 #44447118

order29820
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×ΓL(1,𝔽8)×C71⋊C5
unambiguous semidirect product(C4×C7)⋊(C3×C71⋊C5)
unambiguous semidirect product(C4×C71)⋊(C5×ΓL(1,𝔽8))
unambiguous semidirect product(C4×ΓL(1,𝔽8)×C71)⋊C5
unambiguous semidirect product(C4×C7×C71⋊C5)⋊C3

Splittings

Fitting, HallC4×C7×C71 ⋊ C3×C5
derived, HallC7×C71 ⋊ C3×C4×C5
HallC4×C7×C71⋊C5 ⋊ C3
HallC4×ΓL(1,𝔽8)×C71 ⋊ C5
HallC7×C71⋊C5 ⋊ C3×C4
HallΓL(1,𝔽8)×C71 ⋊ C4×C5
HallC4×C71 ⋊ C5×ΓL(1,𝔽8)
SylowC71 ⋊ C4×C5×ΓL(1,𝔽8)
HallC4×C7 ⋊ C3×C71⋊C5
SylowC7 ⋊ C3×C4×C71⋊C5

Subgroups

subgroupG/H
center, hypercenterC4ΓL(1,𝔽8)×C71⋊C5
commutator, hypocenterC7×C71C3×C4×C5
FrattiniC2C2×ΓL(1,𝔽8)×C71⋊C5
FittingC4×C7×C71C3×C5
socle, cosocleC2×C7×C71C2×C3×C5
prime radicalC2×ΓL(1,𝔽8)×C71⋊C5C2
LCSG ▷ C7×C71
UCSC1 ◁ C4

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1988

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 6);