Finite Group Databasebeta

← Prev (#23778950) Next (#23778952) →

ΓL(1,𝔽8)⋊C4×C121 #23778951

order10164
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C3×C4×C121 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)⋊C4×C121
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C121)
unambiguous semidirect productDic7⋊(C3×C121)
unambiguous semidirect product(Dic7×C121)⋊C3

Splittings

derived, SylowC7 ⋊ C3×C4×C121
HallDic7×C121 ⋊ C3
HallΓL(1,𝔽8)×C121 ⋊ C4
HallC7×C121 ⋊ C3×C4
HallDic7 ⋊ C3×C121
HallΓL(1,𝔽8) ⋊ C4×C121

Subgroups

subgroupG/H
center, hypercenterC2×C121AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C121
FrattiniC2×C11C11×AGL(1,𝔽7)
FittingC2×C7×C121C2×C3
socle, cosocleC2×C7×C11C2×C3×C11
prime radicalC2×C11×ΓL(1,𝔽8)C2×C11
LCSG ▷ C7
UCSC1 ◁ C2×C121

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1694 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×ΓL(1,𝔽8)⋊C4×C121, C121×C3⋊(ΓL(1,𝔽8)⋊C4)
maximal normal subgroup ofC3×ΓL(1,𝔽8)⋊C4×C121
maximal quotient ofC121×Dic7⋊C9, C3×ΓL(1,𝔽8)⋊C4×C121, C121×C3⋊(ΓL(1,𝔽8)⋊C4)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10164, 3);