Finite Group Databasebeta

← Prev (#44447172) Next (#44447174) →

C3×AGL(1,𝔽5)×C71⋊C7 #44447173

order29820
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×AGL(1,𝔽5)×C71⋊C7
unambiguous semidirect product(AGL(1,𝔽5)×C71)⋊(C3×C7)
unambiguous semidirect product(C3×AGL(1,𝔽5)×C71)⋊C7

Splittings

Fitting, socle, HallC3×C5×C71 ⋊ C4×C7
derived, HallC5×C71 ⋊ C3×C4×C7
HallC3×C5×C71⋊C7 ⋊ C4
HallC3×AGL(1,𝔽5)×C71 ⋊ C7
HallC5×C71⋊C7 ⋊ C3×C4
HallAGL(1,𝔽5)×C71 ⋊ C3×C7
HallC3×C71 ⋊ C7×AGL(1,𝔽5)
SylowC71 ⋊ C3×C7×AGL(1,𝔽5)
HallC3×C5 ⋊ C4×C71⋊C7
SylowC5 ⋊ C3×C4×C71⋊C7

Subgroups

subgroupG/H
center, hypercenterC3AGL(1,𝔽5)×C71⋊C7
commutator, hypocenterC5×C71C3×C4×C7
FrattiniC1G
Fitting, socleC3×C5×C71C4×C7
prime radicalC3×D5×C71⋊C7C2
cosocleD5×C71C2×C3×C7
LCSG ▷ C5×C71
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1065

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 61);