Finite Group Databasebeta

← Prev (#26044889) Next (#26044891) →

C3×ΓL(1,𝔽8)⋊Dic47 #26044890

order11844
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)⋊Dic47
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×Dic47)
unambiguous semidirect productC47⋊(C3×ΓL(1,𝔽8)⋊C4)
unambiguous semidirect productDic329⋊C32
unambiguous semidirect product(C3×Dic329)⋊C3

Splittings

derived, HallC7×C47 ⋊ C32×C4
HallC3×ΓL(1,𝔽8)×C47 ⋊ C4
HallDic329 ⋊ C32
HallC3×ΓL(1,𝔽8) ⋊ Dic47
SylowC47 ⋊ C3×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C32×Dic47

Subgroups

subgroupG/H
center, hypercenterC2×C3ΓL(1,𝔽8)⋊D47
commutator, hypocenterC7×C47C32×C4
FrattiniC2C3×ΓL(1,𝔽8)⋊D47
Fitting, socleC2×C3×C7×C47C2×C3
prime radicalC2×C3×ΓL(1,𝔽8)×C47C2
cosocleC2×C7×C47C2×C32
LCSG ▷ C7×C47
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

732 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11844, 37);