Finite Group Databasebeta

← Prev (#34084752) Next (#34084754) →

C4×C11×ΓL(1,𝔽8)2 #34084753

order19404
automorphism?
homologyAbelianization (H1) = C32×C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC4×C11×ΓL(1,𝔽8)2
unambiguous semidirect product(C4×C7×ΓL(1,𝔽8))⋊(C3×C11)
unambiguous semidirect product(C4×#3861)⋊(C3×C11)
unambiguous semidirect product(C4×#3862)⋊(C3×C11)
unambiguous semidirect product(C4×C7×C11×ΓL(1,𝔽8))⋊C3
unambiguous semidirect product(C4×C11×#3861)⋊C3
unambiguous semidirect product(C4×C11×#3862)⋊C3

Splittings

Fitting, HallC4×C72×C11 ⋊ C32
derived, SylowC72 ⋊ C32×C4×C11
HallC72×C11 ⋊ C32×C4
HallC4×C72 ⋊ C32×C11

Subgroups

subgroupG/H
center, hypercenterC4×C11ΓL(1,𝔽8)2
commutator, hypocenterC72C32×C4×C11
FrattiniC2C2×C11×ΓL(1,𝔽8)2
FittingC4×C72×C11C32
socleC2×C72×C11C2×C32
prime radicalC2×C11×ΓL(1,𝔽8)2C2
cosocleC2×C72C2×C32×C11
LCSG ▷ C72
UCSC1 ◁ C4×C11

168 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 924

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19404, 244);