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C71×ΓL(1,𝔽8)⋊AGL(1,𝔽5) #44447202

order29820
automorphism?
homologyAbelianization (H1) = C3×C4×C71 · Schur multiplier (H2) = C1

Aliases

direct productC71×ΓL(1,𝔽8)⋊AGL(1,𝔽5)
unambiguous semidirect productΓL(1,𝔽8)⋊(AGL(1,𝔽5)×C71)
unambiguous semidirect product(C7⋊AGL(1,𝔽5))⋊(C3×C71)
unambiguous semidirect product(C71×C7⋊AGL(1,𝔽5))⋊C3

Splittings

Fitting, socle, HallC5×C7×C71 ⋊ C3×C4
derived, HallC5×C7 ⋊ C3×C4×C71
HallC71×C7⋊AGL(1,𝔽5) ⋊ C3
HallC5×ΓL(1,𝔽8)×C71 ⋊ C4
HallΓL(1,𝔽8)×C71 ⋊ AGL(1,𝔽5)
HallC7×C71 ⋊ C3×AGL(1,𝔽5)
HallC5×C71 ⋊ ΓL(1,𝔽8)⋊C4
HallC7⋊AGL(1,𝔽5) ⋊ C3×C71
HallC5×ΓL(1,𝔽8) ⋊ C4×C71
HallΓL(1,𝔽8) ⋊ AGL(1,𝔽5)×C71
SylowC7 ⋊ C3×AGL(1,𝔽5)×C71
SylowC5 ⋊ C71×ΓL(1,𝔽8)⋊C4

Subgroups

subgroupG/H
center, hypercenterC71ΓL(1,𝔽8)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C3×C4×C71
FrattiniC1G
Fitting, socleC5×C7×C71C3×C4
prime radicalD5×ΓL(1,𝔽8)×C71C2
cosocleC7×D5C2×C3×C71
LCSG ▷ C5×C7
UCSC1 ◁ C71

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2485

Conjugacy classes & character table

1349 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 90);